Abstract

Hyperentangled-Bell-state analysis (HBSA) represents a key step in many quantum information processing schemes that utilize hyperentangled states. In this paper, we present a complete and faithful HBSA scheme for two-photon quantum systems hyperentangled in both the polarization and spatial-mode degrees of freedom, using a failure-heralded and fidelity-robust quantum swap gate for the polarization states of two photons (P-SWAP gate), constructed with a singly charged semiconductor quantum dot (QD) in a double-sided optical microcavity (double-sided QD-cavity system) and some linear-optical elements. Compared with the previously proposed complete HBSA schemes using different auxiliary tools such as parity-check quantum nondemonlition detectors or additional entangled states, our scheme significantly simplifies the analysis process and saves the quantum resource. Unlike the previous schemes based on the ideal optical giant circular birefringence induced by a single-electron spin in a double-sided QD-cavity system, our scheme guarantees the robust fidelity and relaxes the requirement on the QD-cavity parameters. These features indicate that our scheme may be more feasible and useful in practical applications based on the photonic hyperentanglement.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (9)

C.-Y. Gao, B.-C. Ren, Y.-X. Zhang, Q. Ai, and F.-G. Deng, “The linear optical unambiguous discrimination of hyperentangled Bell states assisted by time bin,” Ann. of Phys. 531(10), 1900201 (2019).
[Crossref]

G.-Y. Wang, B.-C. Ren, F.-G. Deng, and G.-L. Long, “Complete analysis of hyperentangled Bell states assisted with auxiliary hyperentanglement,” Opt. Express 27(6), 8994–9003 (2019).
[Crossref]

Q.-H. Song, “Emerging opportunities for ultra-high Q whispering gallery mode microcavities,” Sci. China Phys. Mech. Astron. 62(7), 74231 (2019).
[Crossref]

C. Cao, Y.-H. Han, L. Zhang, L. Fan, Y.-W. Duan, and R. Zhang, “High-fidelity universal quantum controlled gates on electron-spin qubits in quantum dots inside single-sided optical microcavities,” Adv. Quantum Technol. 2(10), 1900081 (2019).
[Crossref]

Y.-Y. Zheng, L.-X. Liang, and M. Zhang, “Error-heralded generation and self-assisted complete analysis of two-photon hyperentangled Bell states through single-sided quantum-dot-cavity systems,” Sci. China Phys. Mech. Astron. 62(7), 970312 (2019).
[Crossref]

J.-Z. Liu, N.-Y. Chen, W.-Q. Liu, H.-R. Wei, and M. Hua, “Hyperparallel transistor, router and dynamic random access memory with unity fidelities,” Opt. Express 27(15), 21380–21394 (2019).
[Crossref]

A.-P. Liu, L.-Y. Cheng, Q. Guo, S.-L. Su, H.-F. Wang, and S. Zhang, “Error-detected single-photon quantum routing using a quantum dot and a double-sided microcavity system,” Chin. Phys. B 28(2), 020301 (2019).
[Crossref]

F.-F. Du, Y.-T. Liu, Z.-R. Shi, Y.-X. Liang, J. Tang, and J. Liu, “Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link,” Opt. Express 27(19), 27046–27061 (2019).
[Crossref]

A.-P. Liu, L.-Y. Cheng, Q. Guo, S.-L. Su, H.-F. Wang, and S. Zhang, “Heralded entanglement concentration of nonlocal photons assisted by doublesided optical microcavities,” Phys. Scr. 94(9), 095103 (2019).
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2018 (8)

G.-Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F.-G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10(5), 054058 (2018).
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G.-Y. Wang, T. Li, Q. Ai, and F.-G. Deng, “Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom,” Opt. Express 26(18), 23333–23346 (2018).
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H.-R. Wei, N.-Y. Chen, and J.-Z. Liu, “Heralded universal quantum gate and entangler assisted by imperfect double-sided quantum-dot-microcavity systems,” Ann. of Phys. 530(8), 1800071 (2018).
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J.-Z. Liu, H.-R. Wei, and N.-Y. Chen, “A heralded and error-rejecting three-photon hyper-parallel quantum gate through cavity-assisted interactions,” Sci. Rep. 8(1), 1885 (2018).
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Z. Zeng, “Self-assisted complete hyperentangled Bell state analysis using quantum-dot spins in optical microcavities,” Laser Phys. Lett. 15(5), 055204 (2018).
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B.-Y. Xia, C. Cao, Y.-H. Han, and R. Zhang, “Universal photonic three-qubit quantum gates with two degrees of freedom assisted by charged quantum dots inside single-sided optical microcavities,” Laser Phys. 28(9), 095201 (2018).
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X.-M. Hu, Y. Guo, B.-H. Liu, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Beating the channel capacity limit for superdense coding with entangled ququarts,” Sci. Adv. 4(7), eaat9304 (2018).
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X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-qubit entanglement with six photons’ three degrees of freedom,” Phys. Rev. Lett. 120(26), 260502 (2018).
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2017 (8)

X.-H. Li and S. Ghose, “Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement,” Phys. Rev. A 96(2), 020303 (2017).
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C. Y. Hu, “Photonic transistor and router using a single quantum-dot-confined spin in a single-sided optical microcavity,” Sci. Rep. 7(1), 45582 (2017).
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C. Cao, Y.-W. Duan, X. Chen, R. Zhang, T.-J. Wang, and C. Wang, “Implementation of single-photon quantum routing and decoupling using a nitrogen-vacancy center and a whispering-gallery-mode resonator-waveguide system,” Opt. Express 25(15), 16931–16946 (2017).
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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(22), 220501 (2017).
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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(12), 120313 (2017).
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2016 (6)

Y.-F. Xiao and Q.-H. Gong, “Optical microcavity: from fundamental physics to functional photonics devices,” Sci. Bull. 61(3), 185–186 (2016).
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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(2), 022302 (2016).
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X.-H. Li and S. Ghose, “Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement,” Opt. Express 24(16), 18388–18398 (2016).
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C. Cao, X. Chen, Y.-W. Duan, L. Fan, R. Zhang, T.-J. Wang, and C. Wang, “Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements,” Sci. China Phys. Mech. Astron. 59(10), 100315 (2016).
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C. Y. Hu, “Spin-based single-photon transistor, dynamic random access memory, diodes, and routers in semiconductors,” Phys. Rev. B 94(24), 245307 (2016).
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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(25), 28444–28458 (2016).
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2015 (5)

A. Reiserer and G. Rempe, “Cavity-based quantum networks with single atoms and optical photons,” Rev. Mod. Phys. 87(4), 1379–1418 (2015).
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T.-J. Wang, L.-L. Liu, R. Zhang, C. Cao, and C. Wang, “One-step hyperentanglement purification and hyperdistillation with linear optics,” Opt. Express 23(7), 9284–9294 (2015).
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D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91(6), 062303 (2015).
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T.-J. Wang and C. Wang, “Parallel quantum computing teleportation for spin qubits in quantum dot and microcavity coupled system,” IEEE J. Sel. Top. Quantum Electron. 21(3), 91–97 (2015).
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X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
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2014 (2)

Y.-B. Sheng and L. Zhou, “Deterministic polarization entanglement purification using time-bin entanglement,” Laser Phys. Lett. 11(8), 085203 (2014).
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B.-C. Ren and G.-L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22(6), 6547–6561 (2014).
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2013 (2)

B.-C. Ren, H.-R. Wei, M. Hua, T. Li, and F.-G. Deng, “Photonic spatial Bell-state analysis for robust quantum secure direct communication using quantum dot-cavity systems,” Eur. Phys. J. D 67(2), 30 (2013).
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Y.-B. Sheng, L. Zhou, W.-W. Cheng, L.-Y. Gong, L. Wang, and S.-M. Zhao, “Complete Bell-state analysis for a single-photon hybrid entangled state,” Chin. Phys. B 22(3), 030314 (2013).
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2012 (3)

2011 (4)

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(2), 022340 (2011).
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C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B 83(11), 115303 (2011).
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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(4), 040305 (2011).
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F.-G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83(6), 062316 (2011).
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2010 (7)

Y.-B. Sheng and F.-G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81(3), 032307 (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(4), 044305 (2010).
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Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82(3), 032318 (2010).
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J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Remote preparation of single-photon "hybrid" entangled and vector-polarization states,” Phys. Rev. Lett. 105(3), 030407 (2010).
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2009 (2)

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science 325(5936), 70–72 (2009).
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C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80(20), 205326 (2009).
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2008 (5)

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B 78(8), 085307 (2008).
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C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78(12), 125318 (2008).
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G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, “Active one-way quantum computation with two-photon four-qubit cluster states,” Phys. Rev. Lett. 100(16), 160502 (2008).
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J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
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J. Berezovsky, M. Mikkelsen, N. Stoltz, L. Coldren, and D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320(5874), 349–352 (2008).
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2007 (5)

M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of faraday rotation from a single confined spin,” Nat. Phys. 3(2), 101–106 (2007).
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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(4), 042317 (2007).
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K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, A. Mair, and J.-W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99(12), 120503 (2007).
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T.-C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75(6), 060305 (2007).
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2006 (3)

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96(19), 190501 (2006).
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A. Greilich, D. Yakovlev, A. Shabaev, A. L. Efros, I. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,” Science 313(5785), 341–345 (2006).
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R. Stevenson, R. Young, P. See, D. Gevaux, K. Cooper, P. Atkinson, I. Farrer, D. Ritchie, and A. Shields, “Magnetic-field-induced reduction of the exciton polarization splitting in InAs quantum dots,” Phys. Rev. B 73(3), 033306 (2006).
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2005 (5)

R. Seguin, A. Schliwa, S. Rodt, K. Pötschke, U. Pohl, and D. Bimberg, “Size-dependent fine-structure splitting in self-organized InAs/GaAs quantum dots,” Phys. Rev. Lett. 95(25), 257402 (2005).
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J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,” Science 309(5744), 2180–2184 (2005).
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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(6), 060302 (2005).
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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(26), 260501 (2005).
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2004 (5)

J. Elzerman, R. Hanson, L. W. Van Beveren, B. Witkamp, L. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,” Nature 430(6998), 431–435 (2004).
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M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,” Nature 432(7013), 81–84 (2004).
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W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. Wieck, “Radiatively limited dephasing in InAs quantum dots,” Phys. Rev. B 70(3), 033301 (2004).
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W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−x as quantum dots by annealing,” Phys. Rev. B 69(16), 161301 (2004).
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J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, T. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot–semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
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2003 (5)

T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, “Spin-based all-optical quantum computation with quantum dots: Understanding and suppressing decoherence,” Phys. Rev. A 68(1), 012310 (2003).
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G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−xGaxAs/GaAs quantum dots,” Phys. Rev. B 67(16), 161306 (2003).
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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(4), 042317 (2003).
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R. Raussendorf, D. E. Browne, and H. J. Briegel, “Measurement-based quantum computation on cluster states,” Phys. Rev. A 68(2), 022312 (2003).
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S. Walborn, S. Pádua, and C. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68(4), 042313 (2003).
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2002 (3)

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A 65(3), 030301 (2002).
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G.-L. Long and X.-S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65(3), 032302 (2002).
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X.-S. Liu, G.-L. Long, D.-M. Tong, and F. Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65(2), 022304 (2002).
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2001 (3)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86(22), 5188–5191 (2001).
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1999 (2)

N. Lütkenhaus, J. Calsamiglia, and K.-A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59(5), 3295–3300 (1999).
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1998 (1)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58(4), R2623–R2626 (1998).
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1997 (2)

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1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, 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(13), 1895–1899 (1993).
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1992 (1)

C. H. Bennett and S. J. Wiesner, “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69(20), 2881–2884 (1992).
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1991 (1)

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D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91(6), 062303 (2015).
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Ai, Q.

C.-Y. Gao, B.-C. Ren, Y.-X. Zhang, Q. Ai, and F.-G. Deng, “The linear optical unambiguous discrimination of hyperentangled Bell states assisted by time bin,” Ann. of Phys. 531(10), 1900201 (2019).
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G.-Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F.-G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10(5), 054058 (2018).
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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(25), 28444–28458 (2016).
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Alsaedi, A.

G.-Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F.-G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10(5), 054058 (2018).
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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(12), 120313 (2017).
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M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of faraday rotation from a single confined spin,” Nat. Phys. 3(2), 101–106 (2007).
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Awschalom, D.

J. Berezovsky, M. Mikkelsen, N. Stoltz, L. Coldren, and D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320(5874), 349–352 (2008).
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M. Atatüre, J. Dreiser, A. Badolato, and A. Imamoglu, “Observation of faraday rotation from a single confined spin,” Nat. Phys. 3(2), 101–106 (2007).
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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(4), 042317 (2007).
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Barreiro, J. T.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Remote preparation of single-photon "hybrid" entangled and vector-polarization states,” Phys. Rev. Lett. 105(3), 030407 (2010).
[Crossref]

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

T.-C. Wei, J. T. Barreiro, and P. G. Kwiat, “Hyperentangled Bell-state analysis,” Phys. Rev. A 75(6), 060305 (2007).
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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(26), 260501 (2005).
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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(6), 060302 (2005).
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A. Greilich, D. Yakovlev, A. Shabaev, A. L. Efros, I. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,” Science 313(5785), 341–345 (2006).
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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(6), 060302 (2005).
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Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, 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(13), 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(20), 2881–2884 (1992).
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Berezovsky, J.

J. Berezovsky, M. Mikkelsen, N. Stoltz, L. Coldren, and D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320(5874), 349–352 (2008).
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Berthiaume, A.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59(3), 1829–1834 (1999).
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G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−xGaxAs/GaAs quantum dots,” Phys. Rev. B 67(16), 161306 (2003).
[Crossref]

Bhatti, D.

D. Bhatti, J. von Zanthier, and G. S. Agarwal, “Entanglement of polarization and orbital angular momentum,” Phys. Rev. A 91(6), 062303 (2015).
[Crossref]

Bichler, M.

M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,” Nature 432(7013), 81–84 (2004).
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Bimberg, D.

R. Seguin, A. Schliwa, S. Rodt, K. Pötschke, U. Pohl, and D. Bimberg, “Size-dependent fine-structure splitting in self-organized InAs/GaAs quantum dots,” Phys. Rev. Lett. 95(25), 257402 (2005).
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Bonato, C.

C. Bonato, F. Haupt, S. S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104(16), 160503 (2010).
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Figures (5)

Fig. 1.
Fig. 1. (a) A singly charged QD in a double-sided optical micropillar cavity. The two distributed Bragg reflectors (DBRs) and the transverse index guiding provide the three-dimensional confinement of light. The two DBRs of the microcavity are made partially reflective (double sided) and symmetric, and the cross section is made circular. (b) The relevant energy levels and the optical spin selection rule for $X^-$ transitions due to the Pauli exclusion principle and the conservation of total spin angular momentum (see text).
Fig. 2.
Fig. 2. Schematic diagram of the error-detected circuit unit constructed with a double-sided QD-cavity system and some linear-optical elements. Here, C is an optical circulator and D is a single-photon detector. BS represents a 50:50 beam splitter, which performs the spatial-mode Hadamard operation [$\left | {{i_1}} \right \rangle \leftrightarrow \left ( {\left | {{j_1}} \right \rangle + \left | {{j_2}} \right \rangle } \right )/\sqrt 2$ and $\left | {{i_2}} \right \rangle \leftrightarrow \left ( {\left | {{j_1}} \right \rangle - \left | {{j_2}} \right \rangle } \right )/\sqrt 2$]. H (H$_{j1}$ or H$_{j2}$) represents a half-wave plate oriented at ${22.5^ \circ }$, which performs the polarization Hadamard operation [$\left | R \right \rangle \leftrightarrow \left ( {\left | R \right \rangle + \left | L \right \rangle } \right )/\sqrt 2$ and $\left | L \right \rangle \leftrightarrow \left ( {\left | R \right \rangle - \left | L \right \rangle } \right )/\sqrt 2$]. M (M$_{j1}$ or M$_{j2}$) is a mirror.
Fig. 3.
Fig. 3. Quantum circuit for the implementation of a failure-heralded and fidelity-robust P-SWAP gate with the error-detected circuit unit. Here, CPBS represents a circularly polarizing beam splitter in the basis $\left \{ {\left | R \right \rangle ,\left | L \right \rangle } \right \}$, which transmits the right-circularly polarized photon component and reflects the left-circularly polarized photon component. X represents a half wave plate oriented at ${45^ \circ }$, which performs the polarization bit-flip operation ${\sigma _x} = \left | R \right \rangle \left \langle L \right | + \left | L \right \rangle \left \langle R \right |$. UBS represents an unbalanced beam splitter with the transmission coefficient $T$. S is an optical switch. Other devices are the same as that in Fig. 2.
Fig. 4.
Fig. 4. Schematic diagram of our complete and faithful HBSA scheme for hyperentangled two-photon systems in the polarization and spatial-mode DOFs.
Fig. 5.
Fig. 5. Calculated success probability of the P-SWAP gate as a function of $g/\kappa$ and $\kappa _s/\kappa$. Here, $\omega = {\omega _c} = {\omega _{{X^ - }}}$ is assumed and $\gamma = 0.1\kappa$ is taken by considering the practical QD-cavity parameters.

Tables (1)

Tables Icon

Table 1. The relationship between the final measurement outcomes of the two photons in the spatial-mode and polarization DOFs and the initial hyperentangled Bell states of the two-photon system. The products of two single-photon hybrid entangled states after the successful P-SWAP operations are also contained in the table, where | ϕ ± A ( B ) p , s = ( | R a 1 ( b 1 ) ± | L a 2 ( b 2 ) ) A ( B ) / 2 and | ψ ± A ( B ) p , s = ( | R a 2 ( b 2 ) ± | L a 1 ( b 1 ) ) A ( B ) / 2 represent the single-photon hybrid entangled states.

Equations (17)

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d a ^ d t = [ i ( ω c ω ) + κ + κ s 2 ] a ^ g σ ^ κ a ^ i n κ a ^ i n + H ^ , d σ ^ d t = [ i ( ω X ω ) + γ 2 ] σ ^ g σ ^ z a ^ + G ^ , a ^ r = a ^ i n + κ a ^ , a ^ t = a ^ i n + κ a ^ ,
r ( ω ) = 1 + t ( ω ) , t ( ω ) = κ [ i ( ω X ω ) + γ 2 ] [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ + κ s 2 ] + g 2 .
r 0 ( ω ) = i ( ω c ω ) + κ s 2 i ( ω c ω ) + κ + κ s 2 , t 0 ( ω ) = κ i ( ω c ω ) + κ + κ s 2 .
| L , r | R , + t | L , , | R , r 0 | L , + t 0 | R , , | R , r | L , + t | R , , | L , r 0 | R , + t 0 | L , , | R , r | L , + t | R , , | L , r 0 | R , + t 0 | L , , | L , r | R , + t | L , , | R , r 0 | L , + t 0 | R , .
| Φ 1 = D | R | i 1 | + + T | L | i 2 | ,
| Ψ 1 = D | R | i 1 | + T | L | i 2 | + .
| φ A = ( α 1 | R + β 1 | L ) A ( χ 1 | a 1 + δ 1 | a 2 ) A , | φ B = ( α 2 | R + β 2 | L ) B ( χ 2 | b 1 + δ 2 | b 2 ) B ,
| Ω 1 = T 2 2 [ α 1 α 2 ( | R R + | R L + | L R + | L L ) A B | + α 1 β 2 ( | R R | R L + | L R | L L ) A B | + β 1 α 2 ( | R R + | R L | L R | L L ) A B | + β 1 β 2 ( | R R | R L | L R + | L L ) A B | ] ( χ 1 | a 1 + δ 1 | a 2 ) A ( χ 2 | b 1 + δ 2 | b 2 ) B .
| Ω 2 = T 4 2 [ ( α 2 | R + β 2 | L ) A ( α 1 | R + β 1 | L ) B | + ( α 2 | R β 2 | L ) A ( α 1 | R β 1 | L ) B | ] ( χ 1 | a 1 + δ 1 | a 2 ) A ( χ 2 | b 1 + δ 2 | b 2 ) B .
| Ω 3 = T 4 ( α 2 | R + β 2 | L ) A ( χ 1 | a 1 + δ 1 | a 2 ) A ( α 1 | R + β 1 | L ) B ( χ 2 | b 1 + δ 2 | b 2 ) B ,
| φ A B p , s = | ε A B p | ξ A B s ,
| ϕ ± A B p = 1 2 ( | R R ± | L L ) A B , | ψ ± A B p = 1 2 ( | R L ± | L R ) A B .
| ϕ ± A B s = 1 2 ( | a 1 b 1 ± | a 2 b 2 ) A B , | ψ ± A B s = 1 2 ( | a 1 b 2 ± | a 2 b 1 ) A B .
| ϕ + p | ϕ + A B s 1 2 ( | R a 1 + | L a 2 ) A 1 2 ( | R b 1 + | L b 2 ) B .
| ϕ + p | ϕ + A B s | a 2 , R A | b 2 , R B , | ϕ p | ϕ + A B s | a 2 , R A | b 2 , L B , | ψ + p | ϕ + A B s | a 2 , R A | b 1 , R B , | ψ p | ϕ + A B s | a 2 , R A | b 1 , L B , | ϕ + p | ϕ A B s | a 2 , L A | b 2 , R B , | ϕ p | ϕ A B s | a 2 , L A | b 2 , L B , | ψ + p | ϕ A B s | a 2 , L A | b 1 , R B , | ψ p | ϕ A B s | a 2 , L A | b 1 , L B , | ϕ + p | ψ + A B s | a 1 , R A | b 2 , R B , | ϕ p | ψ + A B s | a 1 , R A | b 2 , L B , | ψ + p | ψ + A B s | a 1 , R A | b 1 , R B , | ψ p | ψ + A B s | a 1 , R A | b 1 , L B , | ϕ + p | ψ A B s | a 1 , L A | b 2 , R B , | ϕ p | ψ A B s | a 1 , L A | b 2 , L B , | ψ + p | ψ A B s | a 1 , L A | b 1 , R B , | ψ p | ψ A B s | a 1 , L A | b 1 , L B .
| ϕ + A B p | a 1 b 1 1 2 ( | a 2 , R + | a 2 , L ) A | b 2 , R B , | ϕ A B p | a 1 b 1 1 2 ( | a 2 , R + | a 2 , L ) A | b 2 , L B , | ψ + A B p | a 1 b 1 1 2 ( | a 2 , R + | a 2 , L ) A | b 1 , R B , | ψ A B p | a 1 b 1 1 2 ( | a 2 , R + | a 2 , L ) A | b 1 , L B .
η = | T | 8 .

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