Abstract

We present a simple protocol for complete analysis of 16 hyperentangled Bell states of two-photon system in the polarization and the first longitudinal momentum degrees of freedom (DOFs). This complete analysis protocol is accomplished with the auxiliary hyperentangled Bell state in the frequency and the second longitudinal momentum DOFs utilizing the experimentally available optical elements including linear optical elements which manipulate the polarizations and the longitudinal momentums and the optical devices which manipulate frequencies of photons. This complete analysis protocol allows the transmission of log216=4 bits of classical information via quantum hyperdense coding scheme, which is the upper bound of the transmission capacity of the quantum hyperdense coding scheme based on 16 orthogonal hyperentangled Bell states. This complete analysis protocol has a potential to be experimentally realized and is useful for high-capacity quantum communication based on hyperentangled states.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

R. Y. Qi, Z. Sun, Z. S. Lin, P. H. Niu, L. Y. Song, Q. Huang, J. C. Gao, L. G. Yin, and Y. B. Sheng, “Implementation and security analysis of practical quantum secure direct communication,” Light: Sci. & Appl. 8, 22 (2019).
[Crossref]

2018 (2)

P. H. Niu, Z. R. Zhou, Z. S. Lin, Y. B. Sheng, L. G. Yin, and G. L. Long, “Measurement-device-independent quantum communication without encryption,” Sci. Bull. 63, 1345–1350 (2018).
[Crossref]

S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, “Three-step three-party quantum secure direct communication,” Sci. China-Phys. Mech. Astron. 61, 090312 (2018).
[Crossref]

2017 (9)

W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, “Experimental long-distance quantum secure direct communication,” Sci. Bull. 62, 1519–1524 (2017).
[Crossref]

F. G. Deng, B. C. Ren, and X. H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2017).
[Crossref]

B. P. Williams, R. J. Sadlier, and T. S. Humble, “Superdense coding over optical fiber links with complete Bell-state measurements,” Phys. Rev. Lett. 118, 050501 (2017).
[Crossref] [PubMed]

B. C. Ren and F. G. Deng, “Robust hyperparallel photonic quantum entangling gate with cavity QED,” Opt. Express 25, 10863–10873 (2017);
[Crossref] [PubMed]

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
[Crossref]

X. H. Li and S. Ghose, “Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement,” Phys. Rev. A 96, 020303(R) (2017).
[Crossref]

Y. B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sience Bull. 62, 1025–1029 (2017).

Y. H. Kang, Y. H. Chen, Z. C. Shi, B. H. Huang, J. Song, and Y. Xia, “Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm,” Phys. Rev. A 96, 022304 (2017).
[Crossref]

2016 (6)

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
[Crossref] [PubMed]

Q. Liu, G. Y. Wang, Q. Ai, M. Zhang, and F. G. Deng, “Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity,” Sci. Reports 6, 22016 (2016).
[Crossref]

X. H. Li and S. Ghose, “Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity,” Phys. Rev. A 93, 022302 (2016).
[Crossref]

G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, “Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities,” Opt. Express 24, 28444–28458 (2016).
[Crossref] [PubMed]

T. Li and G. L. Long, “Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities,” Phys. Rev. A 94, 022343 (2016).
[Crossref]

H. R. Wei, F. G. Deng, and G. L. Long, “Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities,” Opt. Express 24, 18619–18630 (2016).
[Crossref] [PubMed]

2015 (3)

B. C. Ren, G. Y. Wang, and F. G. Deng, “Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime,” Phys. Rev. A 91, 032328 (2015).
[Crossref]

Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,” Phys. Rev. A 91, 062321 (2015).
[Crossref]

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91, 062303 (2015).
[Crossref]

2014 (1)

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Reports 4, 4623 (2014).
[Crossref]

2013 (1)

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” Laser Phys. Lett. 10, 095202 (2013).
[Crossref]

2012 (3)

Y. Xia, Q. Q. Chen, J. Song, and H. S. Song, “Efficient hyperentangled Greenberger-Horne-Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012).
[Crossref]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24677 (2012).
[Crossref] [PubMed]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
[Crossref]

2011 (4)

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nat. Commun. 2, 537 (2011).
[Crossref]

N. Pisenti, C. P. E. Gaebler, and T. W. Lynn, “Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement,” Phys. Rev. A 84, 022340 (2011).
[Crossref]

T. J. Wang, T. Li, F. F. Du, and F. G. Deng, “High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement,” Chin. Phys. Lett. 28, 040305 (2011).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

2010 (6)

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

B. L. Hu and Y. B. Zhan, “Generation of hyperentangled states between remote noninteracting atomic ions,” Phys. Rev. A 82, 054301 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010)
[Crossref]

2009 (2)

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[Crossref]

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref] [PubMed]

2008 (4)

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[Crossref]

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, “A frequency-coded quantum key distribution scheme,” Opt. Commun. 281, 4800–4802 (2008).
[Crossref]

H. Takesue, “Erasing distinguishability using quantum frequency up-conversion,” Phys. Rev. Lett. 101, 173901 (2008).
[Crossref] [PubMed]

2007 (3)

M. Bloch, S. W. McLaughlin, J. M. Merolla, and F. Patois, “Frequency-coded quantum key distribution,” Opt. Lett. 32, 301–303 (2007).
[Crossref] [PubMed]

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell state analysis,” Phys. Rev. A 75, 060305 (2007).
[Crossref]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[Crossref]

2006 (1)

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[Crossref] [PubMed]

2005 (9)

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[Crossref]

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bellstates analysis using hyper-entanglement,” Phys. Lett. A 343, 8–11 (2005).
[Crossref]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[Crossref]

C. Cinelli, M. Barbieri, F. De Martini, and P. Mataloni, “Realization of hyperentangled two-photon states,” Laser Phys. 15, 124–128 (2005).

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30, 1725–1727 (2005).
[Crossref] [PubMed]

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
[Crossref]

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Coherent analysis of quantum optical sideband modes,” Opt. Lett. 30, 2481–2483 (2005).
[Crossref] [PubMed]

2004 (3)

E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
[Crossref]

A. Yabushita and T. Kobayashi, “Spectroscopy by frequency-entangled photon pairs,” Phys. Rev. A 69, 013806 (2004).
[Crossref]

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,” Fortschr. Phy. 52, 1102–1109 (2004).
[Crossref]

2003 (3)

F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[Crossref]

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[Crossref]

J. Zhang, “Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light,” Phys. Rev. A 67, 054302 (2003).
[Crossref]

2002 (2)

E. H. Huntington and T. C. Ralph, “Separating the quantum sidebands of an optical field,” J. Opt. B: Quantum Semiclassical Opt. 4, 123–128 (2002).
[Crossref]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

1999 (1)

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

1998 (1)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[Crossref]

1993 (1)

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

1992 (2)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Agarwal, G. S.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91, 062303 (2015).
[Crossref]

Ai, Q.

Q. Liu, G. Y. Wang, Q. Ai, M. Zhang, and F. G. Deng, “Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity,” Sci. Reports 6, 22016 (2016).
[Crossref]

G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, “Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities,” Opt. Express 24, 28444–28458 (2016).
[Crossref] [PubMed]

Alzahrani, F.

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
[Crossref]

Barbieri, M.

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[Crossref]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[Crossref]

C. Cinelli, M. Barbieri, F. De Martini, and P. Mataloni, “Realization of hyperentangled two-photon states,” Laser Phys. 15, 124–128 (2005).

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,” Fortschr. Phy. 52, 1102–1109 (2004).
[Crossref]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell state analysis,” Phys. Rev. A 75, 060305 (2007).
[Crossref]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[Crossref]

Barrett, S. D.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

Beausoleil, R. G.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Berthiaume, A.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Bhatti, D.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91, 062303 (2015).
[Crossref]

Bloch, M.

M. Bloch, S. W. McLaughlin, J. M. Merolla, and F. Patois, “Frequency-coded quantum key distribution,” Opt. Lett. 32, 301–303 (2007).
[Crossref] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Bužek, V.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Ceccarelli, R.

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[Crossref]

Chen, Q. Q.

Y. Xia, Q. Q. Chen, J. Song, and H. S. Song, “Efficient hyperentangled Greenberger-Horne-Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012).
[Crossref]

Chen, S. S.

S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, “Three-step three-party quantum secure direct communication,” Sci. China-Phys. Mech. Astron. 61, 090312 (2018).
[Crossref]

Chen, Y. A.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

Chen, Y. H.

Y. H. Kang, Y. H. Chen, Z. C. Shi, B. H. Huang, J. Song, and Y. Xia, “Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm,” Phys. Rev. A 96, 022304 (2017).
[Crossref]

Chen, Z. B.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

Chiuri, A.

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref] [PubMed]

Cinelli, C.

C. Cinelli, M. Barbieri, F. De Martini, and P. Mataloni, “Realization of hyperentangled two-photon states,” Laser Phys. 15, 124–128 (2005).

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[Crossref]

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,” Fortschr. Phy. 52, 1102–1109 (2004).
[Crossref]

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

De Martini, F.

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[Crossref]

A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
[Crossref] [PubMed]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[Crossref]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[Crossref]

C. Cinelli, M. Barbieri, F. De Martini, and P. Mataloni, “Realization of hyperentangled two-photon states,” Laser Phys. 15, 124–128 (2005).

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,” Fortschr. Phy. 52, 1102–1109 (2004).
[Crossref]

Deng, F. G.

B. C. Ren and F. G. Deng, “Robust hyperparallel photonic quantum entangling gate with cavity QED,” Opt. Express 25, 10863–10873 (2017);
[Crossref] [PubMed]

F. G. Deng, B. C. Ren, and X. H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2017).
[Crossref]

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
[Crossref]

Q. Liu, G. Y. Wang, Q. Ai, M. Zhang, and F. G. Deng, “Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity,” Sci. Reports 6, 22016 (2016).
[Crossref]

G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, “Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities,” Opt. Express 24, 28444–28458 (2016).
[Crossref] [PubMed]

H. R. Wei, F. G. Deng, and G. L. Long, “Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities,” Opt. Express 24, 18619–18630 (2016).
[Crossref] [PubMed]

B. C. Ren, G. Y. Wang, and F. G. Deng, “Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime,” Phys. Rev. A 91, 032328 (2015).
[Crossref]

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Reports 4, 4623 (2014).
[Crossref]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” Laser Phys. Lett. 10, 095202 (2013).
[Crossref]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24677 (2012).
[Crossref] [PubMed]

T. J. Wang, T. Li, F. F. Du, and F. G. Deng, “High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement,” Chin. Phys. Lett. 28, 040305 (2011).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010)
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
[Crossref]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[Crossref]

Diamanti, E.

C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30, 1725–1727 (2005).
[Crossref] [PubMed]

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
[Crossref]

Ding, D. S.

W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
[Crossref] [PubMed]

Dong, M. X.

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
[Crossref] [PubMed]

Du, F. F.

T. J. Wang, T. Li, F. F. Du, and F. G. Deng, “High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement,” Chin. Phys. Lett. 28, 040305 (2011).
[Crossref]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Fejer, M. M.

C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30, 1725–1727 (2005).
[Crossref] [PubMed]

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
[Crossref]

Gaebler, C. P. E.

N. Pisenti, C. P. E. Gaebler, and T. W. Lynn, “Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement,” Phys. Rev. A 84, 022340 (2011).
[Crossref]

Gao, J. C.

R. Y. Qi, Z. Sun, Z. S. Lin, P. H. Niu, L. Y. Song, Q. Huang, J. C. Gao, L. G. Yin, and Y. B. Sheng, “Implementation and security analysis of practical quantum secure direct communication,” Light: Sci. & Appl. 8, 22 (2019).
[Crossref]

Gao, W. B.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

Ghose, S.

X. H. Li and S. Ghose, “Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement,” Phys. Rev. A 96, 020303(R) (2017).
[Crossref]

X. H. Li and S. Ghose, “Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity,” Phys. Rev. A 93, 022302 (2016).
[Crossref]

Goebel, A.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

Graham, T. M.

T. M. Graham, C. K. Zeitler, and P. G. Kwiat, “Quantum hyperdense coding,” in Frontiers in Optics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper FTh3D.4.
[Crossref]

Gühne, O.

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

Guo, G. C.

W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
[Crossref] [PubMed]

T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, “A frequency-coded quantum key distribution scheme,” Opt. Commun. 281, 4800–4802 (2008).
[Crossref]

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bellstates analysis using hyper-entanglement,” Phys. Lett. A 343, 8–11 (2005).
[Crossref]

Guo, G. P.

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bellstates analysis using hyper-entanglement,” Phys. Lett. A 343, 8–11 (2005).
[Crossref]

Han, Z. F.

T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, “A frequency-coded quantum key distribution scheme,” Opt. Commun. 281, 4800–4802 (2008).
[Crossref]

Hillery, M.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Hobiny, A.

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
[Crossref]

Honjo, T.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
[Crossref]

Hu, B. L.

B. L. Hu and Y. B. Zhan, “Generation of hyperentangled states between remote noninteracting atomic ions,” Phys. Rev. A 82, 054301 (2010).
[Crossref]

Hua, M.

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24677 (2012).
[Crossref] [PubMed]

Huang, B. H.

Y. H. Kang, Y. H. Chen, Z. C. Shi, B. H. Huang, J. Song, and Y. Xia, “Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm,” Phys. Rev. A 96, 022304 (2017).
[Crossref]

Huang, Q.

R. Y. Qi, Z. Sun, Z. S. Lin, P. H. Niu, L. Y. Song, Q. Huang, J. C. Gao, L. G. Yin, and Y. B. Sheng, “Implementation and security analysis of practical quantum secure direct communication,” Light: Sci. & Appl. 8, 22 (2019).
[Crossref]

Huang, Y. D.

F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, “Experimental long-distance quantum secure direct communication,” Sci. Bull. 62, 1519–1524 (2017).
[Crossref]

Huber, G.

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[Crossref] [PubMed]

Humble, T. S.

B. P. Williams, R. J. Sadlier, and T. S. Humble, “Superdense coding over optical fiber links with complete Bell-state measurements,” Phys. Rev. Lett. 118, 050501 (2017).
[Crossref] [PubMed]

Huntington, E. H.

E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Coherent analysis of quantum optical sideband modes,” Opt. Lett. 30, 2481–2483 (2005).
[Crossref] [PubMed]

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H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
[Crossref]

Vallone, G.

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
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A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
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M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[Crossref]

von Zanthier, J.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91, 062303 (2015).
[Crossref]

Walborn, S. P.

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[Crossref]

Wang, C.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

Wang, G. Y.

G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, “Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities,” Opt. Express 24, 28444–28458 (2016).
[Crossref] [PubMed]

Q. Liu, G. Y. Wang, Q. Ai, M. Zhang, and F. G. Deng, “Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity,” Sci. Reports 6, 22016 (2016).
[Crossref]

B. C. Ren, G. Y. Wang, and F. G. Deng, “Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime,” Phys. Rev. A 91, 032328 (2015).
[Crossref]

Wang, H. B.

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
[Crossref]

Wang, T. J.

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
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T. J. Wang, T. Li, F. F. Du, and F. G. Deng, “High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement,” Chin. Phys. Lett. 28, 040305 (2011).
[Crossref]

Wei, H. R.

H. R. Wei, F. G. Deng, and G. L. Long, “Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities,” Opt. Express 24, 18619–18630 (2016).
[Crossref] [PubMed]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” Laser Phys. Lett. 10, 095202 (2013).
[Crossref]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24677 (2012).
[Crossref] [PubMed]

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
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T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell state analysis,” Phys. Rev. A 75, 060305 (2007).
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Weinfurter, H.

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
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P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
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C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
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B. P. Williams, R. J. Sadlier, and T. S. Humble, “Superdense coding over optical fiber links with complete Bell-state measurements,” Phys. Rev. Lett. 118, 050501 (2017).
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Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
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Wu, F. Z.

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
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Xia, Y.

Y. H. Kang, Y. H. Chen, Z. C. Shi, B. H. Huang, J. Song, and Y. Xia, “Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm,” Phys. Rev. A 96, 022304 (2017).
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Y. Xia, Q. Q. Chen, J. Song, and H. S. Song, “Efficient hyperentangled Greenberger-Horne-Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012).
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Xiong, J.

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
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W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
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A. Yabushita and T. Kobayashi, “Spectroscopy by frequency-entangled photon pairs,” Phys. Rev. A 69, 013806 (2004).
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R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nat. Commun. 2, 537 (2011).
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Yamamoto, Y.

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
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C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30, 1725–1727 (2005).
[Crossref] [PubMed]

Yang, G. J.

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
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W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
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Yin, L. G.

R. Y. Qi, Z. Sun, Z. S. Lin, P. H. Niu, L. Y. Song, Q. Huang, J. C. Gao, L. G. Yin, and Y. B. Sheng, “Implementation and security analysis of practical quantum secure direct communication,” Light: Sci. & Appl. 8, 22 (2019).
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P. H. Niu, Z. R. Zhou, Z. S. Lin, Y. B. Sheng, L. G. Yin, and G. L. Long, “Measurement-device-independent quantum communication without encryption,” Sci. Bull. 63, 1345–1350 (2018).
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Yin, Z. Q.

T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, “A frequency-coded quantum key distribution scheme,” Opt. Commun. 281, 4800–4802 (2008).
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T. M. Graham, C. K. Zeitler, and P. G. Kwiat, “Quantum hyperdense coding,” in Frontiers in Optics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper FTh3D.4.
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B. L. Hu and Y. B. Zhan, “Generation of hyperentangled states between remote noninteracting atomic ions,” Phys. Rev. A 82, 054301 (2010).
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Zhang, J.

J. Zhang, “Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light,” Phys. Rev. A 67, 054302 (2003).
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Zhang, M.

Q. Liu, G. Y. Wang, Q. Ai, M. Zhang, and F. G. Deng, “Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity,” Sci. Reports 6, 22016 (2016).
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Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,” Phys. Rev. A 91, 062321 (2015).
[Crossref]

Zhang, T.

T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, “A frequency-coded quantum key distribution scheme,” Opt. Commun. 281, 4800–4802 (2008).
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Zhang, W.

W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
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F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, “Experimental long-distance quantum secure direct communication,” Sci. Bull. 62, 1519–1524 (2017).
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Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
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Zhong, W.

S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, “Three-step three-party quantum secure direct communication,” Sci. China-Phys. Mech. Astron. 61, 090312 (2018).
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Zhou, H. Y.

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
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Zhou, L.

S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, “Three-step three-party quantum secure direct communication,” Sci. China-Phys. Mech. Astron. 61, 090312 (2018).
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W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
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Y. B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sience Bull. 62, 1025–1029 (2017).

Zhou, Z. R.

P. H. Niu, Z. R. Zhou, Z. S. Lin, Y. B. Sheng, L. G. Yin, and G. L. Long, “Measurement-device-independent quantum communication without encryption,” Sci. Bull. 63, 1345–1350 (2018).
[Crossref]

Zhou, Z. Y.

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
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Zhu, F.

F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, “Experimental long-distance quantum secure direct communication,” Sci. Bull. 62, 1519–1524 (2017).
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Chin. Phys. Lett. (1)

T. J. Wang, T. Li, F. F. Du, and F. G. Deng, “High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement,” Chin. Phys. Lett. 28, 040305 (2011).
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Fortschr. Phy. (1)

M. Barbieri, C. Cinelli, F. De Martini, and P. Mataloni, “Generation of (2×2) and (4×4) two-photon states with tunable degree of entanglement and mixedness,” Fortschr. Phy. 52, 1102–1109 (2004).
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J. Opt. B: Quantum Semiclassical Opt. (1)

E. H. Huntington and T. C. Ralph, “Separating the quantum sidebands of an optical field,” J. Opt. B: Quantum Semiclassical Opt. 4, 123–128 (2002).
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J. Opt. Soc. Am. B (1)

Y. Xia, Q. Q. Chen, J. Song, and H. S. Song, “Efficient hyperentangled Greenberger-Horne-Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012).
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Laser Phys. (1)

C. Cinelli, M. Barbieri, F. De Martini, and P. Mataloni, “Realization of hyperentangled two-photon states,” Laser Phys. 15, 124–128 (2005).

Laser Phys. Lett. (1)

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” Laser Phys. Lett. 10, 095202 (2013).
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Light: Sci. & Appl. (1)

R. Y. Qi, Z. Sun, Z. S. Lin, P. H. Niu, L. Y. Song, Q. Huang, J. C. Gao, L. G. Yin, and Y. B. Sheng, “Implementation and security analysis of practical quantum secure direct communication,” Light: Sci. & Appl. 8, 22 (2019).
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Nat. Commun. (1)

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nat. Commun. 2, 537 (2011).
[Crossref]

Nat. Phys. (2)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

W. B. Gao, C. Y. Lu, X. C. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6, 331–335 (2010).
[Crossref]

New J. Phys. (1)

H. Takesue, E. Diamanti, T. Honjo, C. Langrock, M. M. Fejer, K. Inoue, and Y. Yamamoto, “Differential phase shift quantum key distribution experiment over 105km fibre,” New J. Phys. 7, 232 (2005).
[Crossref]

Opt. Commun. (1)

T. Zhang, Z. Q. Yin, Z. F. Han, and G. C. Guo, “A frequency-coded quantum key distribution scheme,” Opt. Commun. 281, 4800–4802 (2008).
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Opt. Express (4)

B. C. Ren and F. G. Deng, “Robust hyperparallel photonic quantum entangling gate with cavity QED,” Opt. Express 25, 10863–10873 (2017);
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H. R. Wei, F. G. Deng, and G. L. Long, “Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities,” Opt. Express 24, 18619–18630 (2016).
[Crossref] [PubMed]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24677 (2012).
[Crossref] [PubMed]

G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, “Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities,” Opt. Express 24, 28444–28458 (2016).
[Crossref] [PubMed]

Opt. Lett. (3)

C. Langrock, E. Diamanti, R. V. Roussev, Y. Yamamoto, M. M. Fejer, and H. Takesue, “Highly efficient single-photon detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides,” Opt. Lett. 30, 1725–1727 (2005).
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E. H. Huntington, G. N. Milford, C. Robilliard, and T. C. Ralph, “Coherent analysis of quantum optical sideband modes,” Opt. Lett. 30, 2481–2483 (2005).
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M. Bloch, S. W. McLaughlin, J. M. Merolla, and F. Patois, “Frequency-coded quantum key distribution,” Opt. Lett. 32, 301–303 (2007).
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Phys. Lett. A (1)

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bellstates analysis using hyper-entanglement,” Phys. Lett. A 343, 8–11 (2005).
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Phys. Rev. A (30)

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
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Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
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F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
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B. C. Ren, G. Y. Wang, and F. G. Deng, “Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime,” Phys. Rev. A 91, 032328 (2015).
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T. Li and G. L. Long, “Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities,” Phys. Rev. A 94, 022343 (2016).
[Crossref]

B. L. Hu and Y. B. Zhan, “Generation of hyperentangled states between remote noninteracting atomic ions,” Phys. Rev. A 82, 054301 (2010).
[Crossref]

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[Crossref]

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[Crossref]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: Realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[Crossref]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
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Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
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G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
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D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91, 062303 (2015).
[Crossref]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A 78, 022321 (2008).
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F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
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C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

J. Zhang, “Einstein-Podolsky-Rosen sideband entanglement in broadband squeezed light,” Phys. Rev. A 67, 054302 (2003).
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E. H. Huntington and T. C. Ralph, “Components for optical qubits encoded in sideband modes,” Phys. Rev. A 69, 042318 (2004).
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
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Y. H. Kang, Y. H. Chen, Z. C. Shi, B. H. Huang, J. Song, and Y. Xia, “Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm,” Phys. Rev. A 96, 022304 (2017).
[Crossref]

A. Yabushita and T. Kobayashi, “Spectroscopy by frequency-entangled photon pairs,” Phys. Rev. A 69, 013806 (2004).
[Crossref]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010)
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T. C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell state analysis,” Phys. Rev. A 75, 060305 (2007).
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X. H. Li and S. Ghose, “Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement,” Phys. Rev. A 96, 020303(R) (2017).
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T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
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Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,” Phys. Rev. A 91, 062321 (2015).
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X. H. Li and S. Ghose, “Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity,” Phys. Rev. A 93, 022302 (2016).
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Phys. Rev. Lett. (11)

H. Takesue, “Erasing distinguishability using quantum frequency up-conversion,” Phys. Rev. Lett. 101, 173901 (2008).
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Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital angular momentum-entanglement frequency transducer,” Phys. Rev. Lett. 117, 103601 (2016).
[Crossref] [PubMed]

W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
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J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
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C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
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C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
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B. P. Williams, R. J. Sadlier, and T. S. Humble, “Superdense coding over optical fiber links with complete Bell-state measurements,” Phys. Rev. Lett. 118, 050501 (2017).
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A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. 102, 153902 (2009).
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C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
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Sci. Bull. (3)

F. G. Deng, B. C. Ren, and X. H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2017).
[Crossref]

F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, “Experimental long-distance quantum secure direct communication,” Sci. Bull. 62, 1519–1524 (2017).
[Crossref]

P. H. Niu, Z. R. Zhou, Z. S. Lin, Y. B. Sheng, L. G. Yin, and G. L. Long, “Measurement-device-independent quantum communication without encryption,” Sci. Bull. 63, 1345–1350 (2018).
[Crossref]

Sci. China-Phys. Mech. Astron. (2)

S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, “Three-step three-party quantum secure direct communication,” Sci. China-Phys. Mech. Astron. 61, 090312 (2018).
[Crossref]

F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, “High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states,” Sci. China-Phys. Mech. Astron. 60, 120313 (2017).
[Crossref]

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[Crossref]

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[Crossref]

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Y. B. Sheng and L. Zhou, “Distributed secure quantum machine learning,” Sience Bull. 62, 1025–1029 (2017).

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T. M. Graham, C. K. Zeitler, and P. G. Kwiat, “Quantum hyperdense coding,” in Frontiers in Optics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper FTh3D.4.
[Crossref]

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Figures (1)

Fig. 1
Fig. 1 Schematic diagram of the setup for the complete analysis of the 16 hyperentangled Bell states of two-photon system ab. FBS is a frequency beam splitter which divides photon with frequency ω1 or ω2 into spatial mode i1 or i2 (i = a, b), respectively, and FS is a frequency shifter which eliminates the frequency distinguishability. PBS is a polarization beam splitter which transmits the photon in the horizontal polarization state |H〉 and reflects the photon in the vertical polarization state |V〉. HWP is a half-wave plate which performs the Hadamard operation [ | H 1 2 ( | H + | V ) , | V 1 2 ( | H | V ) ] on the polarization DOF of a photon. BS is a 50:50 beam splitter which performs Hadamard operation [ | I 1 2 ( | I + | E ) , | E 1 2 ( | I | E ) ] on the first longitudinal momentum DOF of a photon.

Tables (2)

Tables Icon

Table 1 The relationship between the 16 hyperentangled Bell states in the polarization and the first longitudinal momentum DOFs and the detection results.

Tables Icon

Table 2 The relationship between the classical information, the local unitary operations, and the 16 hyperentangled Bell states in the polarization and the first longitudinal momentum DOFs.

Equations (6)

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| Ψ = | Ψ P | Ψ F | ψ S | ψ Ω .
| ϕ ± P 1 2 ( | H H ± | V V ) , | ψ ± P 1 2 ( | H V ± | V H ) ,
| ϕ ± F 1 2 ( | I I ± | E E ) , | ψ ± F 1 2 ( | I E ± | E I ) ,
| ϕ ± F | ψ S | ϕ ± F 1 2 ( | r r + | l l ) , | ψ ± F | ψ S | ψ ± F 1 2 ( | r l + | l r ) .
| ϕ + P | ψ Ω | ϕ + P 1 2 ( | a 1 b 2 + | a 2 b 1 ) , | ϕ P | ψ Ω | ψ + P 1 2 ( | a 1 b 2 + | a 2 b 1 ) , | ψ + P | ψ Ω | ϕ P 1 2 ( | a 1 b 1 + | a 2 b 2 ) , | ψ P | ψ Ω | ψ P 1 2 ( | a 1 b 1 + | a 2 b 2 ) .
| ϕ + F 1 2 ( | r r + | l l ) | ϕ + F 1 2 ( | r r + | l l ) , | ϕ F 1 2 ( | r r + | l l ) | ψ + F 1 2 ( | r r + | l l ) , | ψ + F 1 2 ( | r l + | l r ) | ϕ F 1 2 ( | r l + | l r ) , | ψ F 1 2 ( | r l + | l r ) | ψ F 1 2 ( | r l + | l r ) .

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