Abstract

As they can travel long distances, free space optical quantum states are good candidates for carrying information in quantum information technology protocols. These states, however, are often complex to produce and require protocols whose success probability drops quickly with an increase of the mean photon number. Here we propose a new protocol for the generation and growth of arbitrary states, based on one by one coherent adjunctions of the simple state superposition α|0〉 + β|1〉. Due to the nature of the protocol, which allows for the use of quantum memories, it can lead to high performances.

© 2014 Optical Society of America

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References

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  1. S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
    [Crossref]
  2. B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
    [Crossref]
  3. K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71(12), 1816–1819 (1993).
    [Crossref] [PubMed]
  4. E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
    [Crossref]
  5. M. Yukawa, K. Miyata, T. Mizuta, H. Yonezawa, P. Marek, R. Filip, and A. Furusawa, “Generating superposition of up-to three photons for continuous variable quantum information processing,” Opt. Express 21(5), 5529–5535 (2013).
    [Crossref] [PubMed]
  6. H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
    [Crossref]
  7. S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
    [Crossref] [PubMed]
  8. A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
    [Crossref]
  9. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
    [Crossref]
  10. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
    [Crossref]
  11. M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
    [Crossref]
  12. J. Fiurášek, R. García-Patrón, and N. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
    [Crossref]
  13. J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
    [Crossref]
  14. K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett. 88(11), 113601 (2002).
    [Crossref] [PubMed]
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    [Crossref]
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  17. A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
    [Crossref] [PubMed]
  18. E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
    [Crossref] [PubMed]
  19. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
    [Crossref] [PubMed]
  20. O. Morin, V. D’Auria, C. Fabre, and J. Laurat, “High-fidelity single-photon source based on a type II optical parametric oscillator,” Opt. Lett. 37(17), 3738–3740 (2012).
    [Crossref] [PubMed]

2014 (2)

J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
[Crossref]

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

2013 (3)

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

M. Yukawa, K. Miyata, T. Mizuta, H. Yonezawa, P. Marek, R. Filip, and A. Furusawa, “Generating superposition of up-to three photons for continuous variable quantum information processing,” Opt. Express 21(5), 5529–5535 (2013).
[Crossref] [PubMed]

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

2012 (1)

2010 (2)

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
[Crossref]

2008 (1)

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

2007 (1)

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
[Crossref]

2006 (2)

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

2005 (1)

J. Fiurášek, R. García-Patrón, and N. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
[Crossref]

2004 (1)

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

2002 (1)

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett. 88(11), 113601 (2002).
[Crossref] [PubMed]

1999 (1)

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
[Crossref]

1993 (1)

K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71(12), 1816–1819 (1993).
[Crossref] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref] [PubMed]

1826 (1)

N. H. Abel, “Beweis der Unmöglichkeit algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen,” Journal für die reine und angewandte Mathematik 1, 65–84 (1826).
[Crossref]

Abel, N. H.

N. H. Abel, “Beweis der Unmöglichkeit algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen,” Journal für die reine und angewandte Mathematik 1, 65–84 (1826).
[Crossref]

Akulin, V. M.

K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71(12), 1816–1819 (1993).
[Crossref] [PubMed]

Andersen, U. L.

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

Babichev, S. A.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

Bernu, J.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Bimbard, E.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
[Crossref]

Blandino, R.

J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
[Crossref]

Boddeda, R.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

Brezger, B.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

Brune, M.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Calkins, B.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Cerf, N.

J. Fiurášek, R. García-Patrón, and N. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
[Crossref]

Clausen, J.

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
[Crossref]

Clement, T. S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

D’Auria, V.

Dakna, M.

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
[Crossref]

Deléglise, S.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Devoret, M. H.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Dotsenko, I.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Etesse, J.

J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
[Crossref]

Fabre, C.

Filip, R.

Fiurášek, J.

J. Fiurášek, R. García-Patrón, and N. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
[Crossref]

Frunzio, L.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Furusawa, A.

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

M. Yukawa, K. Miyata, T. Mizuta, H. Yonezawa, P. Marek, R. Filip, and A. Furusawa, “Generating superposition of up-to three photons for continuous variable quantum information processing,” Opt. Express 21(5), 5529–5535 (2013).
[Crossref] [PubMed]

García-Patrón, R.

J. Fiurášek, R. García-Patrón, and N. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
[Crossref]

Gerrits, T.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Girvin, S. M.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Glancy, S.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Grangier, P.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

Grankin, A.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

Grosse, N. B.

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

Haroche, S.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref] [PubMed]

Jain, N.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
[Crossref]

Jeong, H.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
[Crossref]

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

Kanseri, B.

J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
[Crossref]

Kirchmair, G.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Knill, E.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Knöll, L.

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
[Crossref]

Kragh, C.

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

Kurata, S.

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

Laghaout, A.

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

Lam, P. K.

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

Lance, A. M.

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

Laurat, J.

Leghtas, Z.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Lita, A. E.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Lundeen, J. S.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett. 88(11), 113601 (2002).
[Crossref] [PubMed]

Lvovsky, A. I.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
[Crossref]

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

MacRae, A.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
[Crossref]

Makino, K.

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref] [PubMed]

Marek, P.

Migdall, A. L.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Miller, A. J.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Mirin, R. P.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Mirrahimi, M.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Miyata, K.

Mizuta, T.

Morin, O.

Nam, S. W.

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

Neergaard-Nielsen, J. S.

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

Nigg, S. E.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref] [PubMed]

Ourjoumtsev, A.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

Parigi, V.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

Raimond, J.-M.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Ralph, T. C.

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

Resch, K. J.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett. 88(11), 113601 (2002).
[Crossref] [PubMed]

Rigas, I.

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

Sayrin, C.

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

Schleich, W. P.

K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71(12), 1816–1819 (1993).
[Crossref] [PubMed]

Schoelkopf, R. J.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Stanojevic, J.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

Steinberg, A. M.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett. 88(11), 113601 (2002).
[Crossref] [PubMed]

Symul, T.

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

Tipsmark, A.

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

Tualle-Brouri, R.

J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
[Crossref]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
[Crossref]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

van Loock, P.

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

Vitrant, N.

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

Vlastakis, B.

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

Vogel, K.

K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71(12), 1816–1819 (1993).
[Crossref] [PubMed]

Welsh, D.-G.

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
[Crossref]

Yonezawa, H.

Yoshikawa, J.-I.

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

Yukawa, M.

Journal für die reine und angewandte Mathematik (1)

N. H. Abel, “Beweis der Unmöglichkeit algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen,” Journal für die reine und angewandte Mathematik 1, 65–84 (1826).
[Crossref]

Nat. Phot. (1)

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Phot. 4, 243–247 (2010).
[Crossref]

Nature (London) (2)

S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature (London) 455, 510–514 (2008).
[Crossref]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature (London) 448, 784–786 (2007).
[Crossref]

New J. Phys. (1)

J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, “Proposal for a loophole-free violation of Bell’s inequalities with a set of single photons and homodyne measurements,” New J. Phys. 16, 053001 (2014).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (5)

H. Jeong, A. M. Lance, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, “Conditional quantum-state engineering using ancillary squeezed-vacuum states,” Phys. Rev. A 74, 033813 (2006).
[Crossref]

A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013).
[Crossref]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).
[Crossref]

M. Dakna, J. Clausen, L. Knöll, and D.-G. Welsh, “Generation of arbitrary quantum states of traveling fields,” Phys. Rev. A 59(2), 1658–1661 (1999).
[Crossref]

J. Fiurášek, R. García-Patrón, and N. Cerf, “Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions,” Phys. Rev. A 72, 033822 (2005).
[Crossref]

Phys. Rev. Lett. (6)

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett. 88(11), 113601 (2002).
[Crossref] [PubMed]

K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71(12), 1816–1819 (1993).
[Crossref] [PubMed]

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

E. Bimbard, R. Boddeda, N. Vitrant, A. Grankin, V. Parigi, J. Stanojevic, A. Ourjoumtsev, and P. Grangier, “Homodyne tomography of a single photon retrieved on demand from a cavity-enhanced cold atom memory,” Phys. Rev. Lett. 112, 033601 (2014).
[Crossref] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref] [PubMed]

Phys. Rev. X (1)

J.-I. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, “Creation, storage, and on-demand release of optical quantum states with a negative Wigner function,” Phys. Rev. X 3, 041028 (2013).

Other (1)

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science342, 6158607–610 (2013).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Elementary protocol for generation and growth of arbitrary states: two states | ψ 1 ( 1 ) and | ψ 2 ( 1 ) of the form of Eq. (1) are mixed on a beamsplitter with transmission τ1. A homodyne measurement is performed in one output arm, and the generation of a state |ψout〉 in the other arm is conditioned upon the homodyne event x′ = x′1.
Fig. 2
Fig. 2 Setup for the generation of arbitrary superposition of n photons, in a cascaded configuration.
Fig. 3
Fig. 3 Advantage of the symmetrized configuration. (a) Setup of a symmetrized configuration, in the case where n = 2p. The positions of quantum memories have been specified by the parenthesis symbols (). (b) Total success probability of a protocol involving eight input resource states given by Eq. (1) in a cascaded (solid blue line) and a symmetrical (dashed green line) configuration. The total success probability of a protocol not using any quantum memory is shown for comparison (dot-dashed red line).
Fig. 4
Fig. 4 Optimization of the success probability. (a) Success probability of the protocol for the generation of the state 2−1/2(|1〉 + |2〉) as a function of the quadrature conditioning x′1 = x′0 and the energy transmission of the beamsplitter τ 1 2 = τ 2. The coefficients of the resource states are given by Eq. (11), and the target fidelity is 90%. (b) Optimized success probability for the states is shown as: Eq. (13) solid blue, Eq. (14) dashed red, Eq. (15) dot-dashed green and Eq. (16) solid thin black.
Fig. 5
Fig. 5 Influence of imperfections of (a) photons and (b) homodyne detections on the quality of the output state for cases c′0 = 0 (solid blue line), c′0 = 1 (red dot-dashed line) and c 0 = 1 / 2 (dashed green line).

Equations (24)

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| ψ ( 1 ) = α | 0 + β | 1 .
ψ out ( x ) ( a 1 x b 1 ) ( a 2 x b 2 ) e x 2 2 ,
ψ ( n ) ( x ) P n ( x ) e x 2 2
ψ ( m ) ( x ) P m ( x ) e x 2 2 ,
ψ out ( x ) P n ( τ 1 x ρ 1 x 1 ) P m ( τ 1 x 1 + ρ 1 x ) e x 2 2 .
| ψ out ( a 1 x b 1 ) ( a 2 x b 2 ) ( a n x b n ) e x 2 2 ,
a 1 = 2 β 1 i = 1 n 1 τ i
a j = 2 β j ρ j 1 i = j n 1 τ i for 1 < j < n
a n = 2 β n ρ n 1
b 1 = α 1 + 2 β 1 [ ρ 1 x 1 + l = 1 n 1 i = 1 l τ i ρ l + 1 x n + 1 ]
b j = α j 2 β j τ j 1 x j 1 + 2 β j ρ j 1 [ ρ j x j + l = j n 2 i = j l τ i ρ l + 1 x l + 1 ] for 1 < j < n 1
b n 1 = α n 1 2 β n 1 τ n 2 x n 2 + 2 β n 1 ρ n 2 ρ n 1 x n 1
b n = α n 2 β n τ n 1 x n 1 .
k = 1 n [ x b k a k ] = k = 0 n c k c n 2 n + k 2 n ! k ! H k ( x ) .
| ψ targ = 1 1 + | c 0 | 2 + | c 1 | 2 ( c 0 | 0 + c 1 | 1 + | 2 ) .
ψ targ ( x ) [ x 2 + c 1 x + c 0 2 1 2 ] e x 2 2 .
β 1 = ε 1 1 1 + 2 [ x 1 τ 1 + ρ 1 x 1 ] 2 , α 1 = 1 | β 1 | 2 ,
β 2 = ε 2 1 1 + 2 [ x 2 ρ 1 τ 1 x 1 ] 2 , α 2 = 1 | β 2 | 2 ,
( x x 1 + ρ 2 x 2 τ 2 ) ( x x 1 + ρ 2 x 2 τ 2 ) ( x + τ 2 x 2 ρ 2 ) = x ( x 3 / 2 ) ( x + 3 / 2 ) .
| ψ 1 = | 2
| ψ 2 = 1 2 ( | 1 + | 2 )
| ψ 3 = 1 2 ( | 0 + | 2 )
| ψ 4 = 1 3 ( | 0 + | 1 + | 2 ) ,
| ψ = η phot | 1 1 | + ( 1 η phot ) | 0 0 | .

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