Abstract

Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a “hybrid” approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment. The increase of photon loss decreases this bound, and teleportation better than this limit is impossible even when the squeezing degree of the teleportation channel becomes infinity. Our result indicates that the hybrid scheme can be valid for fault-tolerant quantum computing only when the photon loss rate can be suppressed under a certain limit.

© 2019 Chinese Laser Press

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High-fidelity teleportation of continuous-variable quantum states with discrete-variable resources

Kevin Marshall and Daniel F. V. James
J. Opt. Soc. Am. B 31(3) 423-428 (2014)

References

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    [Crossref]
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    [Crossref]
  32. A. Lund, T. Ralph, and H. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
    [Crossref]
  33. D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
    [Crossref]
  34. S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,” Phys. Rev. A 87, 022326 (2013).
    [Crossref]
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2018 (1)

2015 (2)

S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,” Phys. Rev. Lett. 114, 113603 (2015).
[Crossref]

Y. Li, P. C. Humphreys, G. J. Mendoza, and S. C. Benjamin, “Resource costs for fault-tolerant linear optical quantum computing,” Phys. Rev. X 5, 041007 (2015).
[Crossref]

2014 (2)

F. Ewert and P. van Loock, “3/4-efficient bell measurement with passive linear optics and unentangled ancillae,” Phys. Rev. Lett. 113, 140403 (2014).
[Crossref]

N. C. Menicucci, “Fault-tolerant measurement-based quantum computing with continuous-variable cluster states,” Phys. Rev. Lett. 112, 120504 (2014).
[Crossref]

2013 (4)

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,” Phys. Rev. A 87, 022326 (2013).
[Crossref]

H. A. Zaidi and P. van Loock, “Beating the one-half limit of ancilla-free linear optics Bell measurements,” Phys. Rev. Lett. 110, 260501 (2013).
[Crossref]

2011 (2)

W. P. Grice, “Arbitrarily complete Bell-state measurement using only linear optical elements,” Phys. Rev. A 84, 042331 (2011).
[Crossref]

C.-W. Lee and H. Jeong, “Quantification of macroscopic quantum superpositions within phase space,” Phys. Rev. Lett. 106, 220401 (2011).
[Crossref]

2010 (1)

D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
[Crossref]

2008 (1)

A. Lund, T. Ralph, and H. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
[Crossref]

2006 (2)

C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise thresholds for optical quantum computers,” Phys. Rev. Lett. 96, 020501 (2006).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

2004 (1)

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

2003 (1)

K. Audenaert, M. Plenio, and J. Eisert, “Entanglement cost under positive-partial-transpose-preserving operations,” Phys. Rev. Lett. 90, 027901 (2003).
[Crossref]

2002 (2)

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

T. Ide, H. F. Hofmann, A. Furusawa, and T. Kobayashi, “Gain tuning and fidelity in continuous-variable quantum teleportation,” Phys. Rev. A 65, 062303 (2002).
[Crossref]

2001 (2)

T. Ralph, “Interferometric tests of teleportation,” Phys. Rev. A 65, 012319 (2001).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

2000 (2)

H. F. Hofmann, T. Ide, T. Kobayashi, and A. Furusawa, “Fidelity and information in the quantum teleportation of continuous variables,” Phys. Rev. A 62, 062304 (2000).
[Crossref]

H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000).
[Crossref]

1999 (4)

D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[Crossref]

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

R. Polkinghorne and T. Ralph, “Continuous variable entanglement swapping,” Phys. Rev. Lett. 83, 2095–2099 (1999).
[Crossref]

S. Lloyd and S. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

1998 (3)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58, 883–892 (1998).
[Crossref]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1994 (1)

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[Crossref]

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, 1895–1899 (1993).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Adesso, G.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

Audenaert, K.

K. Audenaert, M. Plenio, and J. Eisert, “Entanglement cost under positive-partial-transpose-preserving operations,” Phys. Rev. Lett. 90, 027901 (2003).
[Crossref]

Benjamin, S. C.

Y. Li, P. C. Humphreys, G. J. Mendoza, and S. C. Benjamin, “Resource costs for fault-tolerant linear optical quantum computing,” Phys. Rev. X 5, 041007 (2015).
[Crossref]

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, 1895–1899 (1993).
[Crossref]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Brassard, G.

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, 1895–1899 (1993).
[Crossref]

Braunstein, S.

S. Lloyd and S. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

Braunstein, S. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

Calsamiglia, J.

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

Chuang, I. L.

D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[Crossref]

Crépeau, C.

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, 1895–1899 (1993).
[Crossref]

Dawson, C. M.

C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise thresholds for optical quantum computers,” Phys. Rev. Lett. 96, 020501 (2006).
[Crossref]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Eisert, J.

K. Audenaert, M. Plenio, and J. Eisert, “Entanglement cost under positive-partial-transpose-preserving operations,” Phys. Rev. Lett. 90, 027901 (2003).
[Crossref]

Ewert, F.

F. Ewert and P. van Loock, “3/4-efficient bell measurement with passive linear optics and unentangled ancillae,” Phys. Rev. Lett. 113, 140403 (2014).
[Crossref]

Fowler, A. G.

D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
[Crossref]

Fuchs, C. A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

Furusawa, A.

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

T. Ide, H. F. Hofmann, A. Furusawa, and T. Kobayashi, “Gain tuning and fidelity in continuous-variable quantum teleportation,” Phys. Rev. A 65, 062303 (2002).
[Crossref]

H. F. Hofmann, T. Ide, T. Kobayashi, and A. Furusawa, “Fidelity and information in the quantum teleportation of continuous variables,” Phys. Rev. A 62, 062304 (2000).
[Crossref]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

Fuwa, M.

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

Gottesman, D.

D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[Crossref]

Grice, W. P.

W. P. Grice, “Arbitrarily complete Bell-state measurement using only linear optical elements,” Phys. Rev. A 84, 042331 (2011).
[Crossref]

Gu, M.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

Haselgrove, H.

A. Lund, T. Ralph, and H. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
[Crossref]

Haselgrove, H. L.

C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise thresholds for optical quantum computers,” Phys. Rev. Lett. 96, 020501 (2006).
[Crossref]

Herrera-Marti, D. A.

D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
[Crossref]

Hofmann, H. F.

T. Ide, H. F. Hofmann, A. Furusawa, and T. Kobayashi, “Gain tuning and fidelity in continuous-variable quantum teleportation,” Phys. Rev. A 65, 062303 (2002).
[Crossref]

H. F. Hofmann, T. Ide, T. Kobayashi, and A. Furusawa, “Fidelity and information in the quantum teleportation of continuous variables,” Phys. Rev. A 62, 062304 (2000).
[Crossref]

Horodecki, P.

K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58, 883–892 (1998).
[Crossref]

Humphreys, P. C.

Y. Li, P. C. Humphreys, G. J. Mendoza, and S. C. Benjamin, “Resource costs for fault-tolerant linear optical quantum computing,” Phys. Rev. X 5, 041007 (2015).
[Crossref]

Ide, T.

T. Ide, H. F. Hofmann, A. Furusawa, and T. Kobayashi, “Gain tuning and fidelity in continuous-variable quantum teleportation,” Phys. Rev. A 65, 062303 (2002).
[Crossref]

H. F. Hofmann, T. Ide, T. Kobayashi, and A. Furusawa, “Fidelity and information in the quantum teleportation of continuous variables,” Phys. Rev. A 62, 062304 (2000).
[Crossref]

Illuminati, F.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

Jennings, D.

D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
[Crossref]

Jeong, H.

S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,” Phys. Rev. Lett. 114, 113603 (2015).
[Crossref]

S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,” Phys. Rev. A 87, 022326 (2013).
[Crossref]

C.-W. Lee and H. Jeong, “Quantification of macroscopic quantum superpositions within phase space,” Phys. Rev. Lett. 106, 220401 (2011).
[Crossref]

H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000).
[Crossref]

Jozsa, R.

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, 1895–1899 (1993).
[Crossref]

Kim, M. S.

H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000).
[Crossref]

Kimble, H. J.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Kobayashi, T.

T. Ide, H. F. Hofmann, A. Furusawa, and T. Kobayashi, “Gain tuning and fidelity in continuous-variable quantum teleportation,” Phys. Rev. A 65, 062303 (2002).
[Crossref]

H. F. Hofmann, T. Ide, T. Kobayashi, and A. Furusawa, “Fidelity and information in the quantum teleportation of continuous variables,” Phys. Rev. A 62, 062304 (2000).
[Crossref]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Lee, C.-W.

C.-W. Lee and H. Jeong, “Quantification of macroscopic quantum superpositions within phase space,” Phys. Rev. Lett. 106, 220401 (2011).
[Crossref]

Lee, J.

H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000).
[Crossref]

Lee, S.-W.

S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,” Phys. Rev. Lett. 114, 113603 (2015).
[Crossref]

S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,” Phys. Rev. A 87, 022326 (2013).
[Crossref]

Lewenstein, M.

K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58, 883–892 (1998).
[Crossref]

Li, Y.

Y. Li, P. C. Humphreys, G. J. Mendoza, and S. C. Benjamin, “Resource costs for fault-tolerant linear optical quantum computing,” Phys. Rev. X 5, 041007 (2015).
[Crossref]

Lloyd, S.

S. Lloyd and S. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

Lund, A.

A. Lund, T. Ralph, and H. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
[Crossref]

Lütkenhaus, N.

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

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Mendoza, G. J.

Y. Li, P. C. Humphreys, G. J. Mendoza, and S. C. Benjamin, “Resource costs for fault-tolerant linear optical quantum computing,” Phys. Rev. X 5, 041007 (2015).
[Crossref]

Menicucci, N. C.

N. C. Menicucci, “Fault-tolerant measurement-based quantum computing with continuous-variable cluster states,” Phys. Rev. Lett. 112, 120504 (2014).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Mizuta, T.

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

Nielsen, M. A.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise thresholds for optical quantum computers,” Phys. Rev. Lett. 96, 020501 (2006).
[Crossref]

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Park, K.

S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,” Phys. Rev. Lett. 114, 113603 (2015).
[Crossref]

Peres, A.

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, 1895–1899 (1993).
[Crossref]

Plenio, M.

K. Audenaert, M. Plenio, and J. Eisert, “Entanglement cost under positive-partial-transpose-preserving operations,” Phys. Rev. Lett. 90, 027901 (2003).
[Crossref]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Polkinghorne, R.

R. Polkinghorne and T. Ralph, “Continuous variable entanglement swapping,” Phys. Rev. Lett. 83, 2095–2099 (1999).
[Crossref]

Polzik, E. S.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

Pryde, G. J.

T. C. Ralph and G. J. Pryde, “Optical quantum computation,” in Progress in Optics (Elsevier, 2010), Vol. 54, pp. 209–269.

Ralph, T.

A. Lund, T. Ralph, and H. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
[Crossref]

T. Ralph, “Interferometric tests of teleportation,” Phys. Rev. A 65, 012319 (2001).
[Crossref]

R. Polkinghorne and T. Ralph, “Continuous variable entanglement swapping,” Phys. Rev. Lett. 83, 2095–2099 (1999).
[Crossref]

Ralph, T. C.

S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,” Phys. Rev. Lett. 114, 113603 (2015).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

T. C. Ralph and G. J. Pryde, “Optical quantum computation,” in Progress in Optics (Elsevier, 2010), Vol. 54, pp. 209–269.

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Rudolph, T.

D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
[Crossref]

Sanpera, A.

K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58, 883–892 (1998).
[Crossref]

Schnabel, R.

Schönbeck, A.

Serafini, A.

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

Suominen, K.-A.

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

Takeda, S.

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

Thies, F.

Vaidman, L.

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[Crossref]

van Loock, P.

F. Ewert and P. van Loock, “3/4-efficient bell measurement with passive linear optics and unentangled ancillae,” Phys. Rev. Lett. 113, 140403 (2014).
[Crossref]

H. A. Zaidi and P. van Loock, “Beating the one-half limit of ancilla-free linear optics Bell measurements,” Phys. Rev. Lett. 110, 260501 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

Vidal, G.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

Weedbrook, C.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

Weinfurter, H.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Werner, R. F.

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

Wootters, W. K.

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, 1895–1899 (1993).
[Crossref]

Yonezawa, H.

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

Zaidi, H. A.

H. A. Zaidi and P. van Loock, “Beating the one-half limit of ancilla-free linear optics Bell measurements,” Phys. Rev. Lett. 110, 260501 (2013).
[Crossref]

Zeilinger, A.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Zyczkowski, K.

K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58, 883–892 (1998).
[Crossref]

Nature (4)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature 402, 390–393 (1999).
[Crossref]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, and A. Furusawa, “Deterministic quantum teleportation of photonic quantum bits by a hybrid technique,” Nature 500, 315–318 (2013).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Phys. Rev. A (13)

T. Ide, H. F. Hofmann, A. Furusawa, and T. Kobayashi, “Gain tuning and fidelity in continuous-variable quantum teleportation,” Phys. Rev. A 65, 062303 (2002).
[Crossref]

K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58, 883–892 (1998).
[Crossref]

G. Adesso, A. Serafini, and F. Illuminati, “Extremal entanglement and mixedness in continuous variable systems,” Phys. Rev. A 70, 022318 (2004).
[Crossref]

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002).
[Crossref]

H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000).
[Crossref]

S. Takeda, T. Mizuta, M. Fuwa, H. Yonezawa, P. van Loock, and A. Furusawa, “Gain tuning for continuous-variable quantum teleportation of discrete-variable states,” Phys. Rev. A 88, 042327 (2013).
[Crossref]

H. F. Hofmann, T. Ide, T. Kobayashi, and A. Furusawa, “Fidelity and information in the quantum teleportation of continuous variables,” Phys. Rev. A 62, 062304 (2000).
[Crossref]

D. A. Herrera-Marti, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332 (2010).
[Crossref]

S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits,” Phys. Rev. A 87, 022326 (2013).
[Crossref]

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

W. P. Grice, “Arbitrarily complete Bell-state measurement using only linear optical elements,” Phys. Rev. A 84, 042331 (2011).
[Crossref]

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[Crossref]

T. Ralph, “Interferometric tests of teleportation,” Phys. Rev. A 65, 012319 (2001).
[Crossref]

Phys. Rev. Lett. (13)

R. Polkinghorne and T. Ralph, “Continuous variable entanglement swapping,” Phys. Rev. Lett. 83, 2095–2099 (1999).
[Crossref]

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, 1895–1899 (1993).
[Crossref]

S. Lloyd and S. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).
[Crossref]

F. Ewert and P. van Loock, “3/4-efficient bell measurement with passive linear optics and unentangled ancillae,” Phys. Rev. Lett. 113, 140403 (2014).
[Crossref]

S.-W. Lee, K. Park, T. C. Ralph, and H. Jeong, “Nearly deterministic Bell measurement for multiphoton qubits and its application to quantum information processing,” Phys. Rev. Lett. 114, 113603 (2015).
[Crossref]

H. A. Zaidi and P. van Loock, “Beating the one-half limit of ancilla-free linear optics Bell measurements,” Phys. Rev. Lett. 110, 260501 (2013).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

C.-W. Lee and H. Jeong, “Quantification of macroscopic quantum superpositions within phase space,” Phys. Rev. Lett. 106, 220401 (2011).
[Crossref]

N. C. Menicucci, “Fault-tolerant measurement-based quantum computing with continuous-variable cluster states,” Phys. Rev. Lett. 112, 120504 (2014).
[Crossref]

K. Audenaert, M. Plenio, and J. Eisert, “Entanglement cost under positive-partial-transpose-preserving operations,” Phys. Rev. Lett. 90, 027901 (2003).
[Crossref]

C. M. Dawson, H. L. Haselgrove, and M. A. Nielsen, “Noise thresholds for optical quantum computers,” Phys. Rev. Lett. 96, 020501 (2006).
[Crossref]

A. Lund, T. Ralph, and H. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
[Crossref]

Phys. Rev. X (1)

Y. Li, P. C. Humphreys, G. J. Mendoza, and S. C. Benjamin, “Resource costs for fault-tolerant linear optical quantum computing,” Phys. Rev. X 5, 041007 (2015).
[Crossref]

Science (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref]

Other (1)

T. C. Ralph and G. J. Pryde, “Optical quantum computation,” in Progress in Optics (Elsevier, 2010), Vol. 54, pp. 209–269.

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Figures (4)

Fig. 1.
Fig. 1. Fidelity change over the gain value g between 2 and 2 with a varying amount of losses in the two-mode squeezed state.
Fig. 2.
Fig. 2. Fidelity curves over the gain value g between 2 and 2 changing as the loss rate r2 increases.
Fig. 3.
Fig. 3. Transmission fidelity of a photonic qubit with numerically optimized gains. Here, q is the squeezing parameter of the initial two-mode squeezed state; the maximum fidelity curve is numerically obtained and plotted with the thick dashed curve, and that of q=1 is plotted with the thin dotted curve. It is impossible to attain fidelity higher than the classical limit (horizontal dotted line) with loss bigger than about 11%.
Fig. 4.
Fig. 4. Log negativity of the two-mode squeezed state in terms of the loss rate r2. On the contrary to the fidelity, there is no inversion in order with increasing loss.

Equations (43)

Equations on this page are rendered with MathJax. Learn more.

|βA,R=1πn=0D^A(β)|n,nA,R,
|qR,B=1q2n=0qn|n,nR,B.
|ψB=1q2πn=0qn|nBn|AD^A(β)|ψA.
|ψout(β)B=T^qg(β)|ψA,
T^qg(β)=1q2πn=0qnD^B(gβ)|nBn|AD^A(β).
TrE1E2(UAE1BSUBE2BS|qq|AB|0000|E1E2UAE1BSUBE2BS),
ϕchannel=(1q2)n,mk,l=max{0,nm}ncnmklqn+mt2(mn)+2(k+l)r4n2(k+l)|klmn+k,mn+l|,
cnmkl=(nk)(nl)(mnk)(mnl)
ρB,out(β)=D^B(gβ)β|AR(|ψψ|AϕRB,channel)|βARD^B.
T^kl(β)=1q2πn=max(k,l)qn(nk)(nl)t2n(k+l)rk+lD^(gβ)|nlnk|D(β),
ρout(β)=k,l=0T^kl(β)|ψψ|T^kl(β).
k,l=0d2β  T^kl(β)T^kl(β)=1.
F=k,lFkl=k,ld2β|ψ|T^kl(β)|ψ|2,
F00=1q2(1+g2)(1q2r2)2gq(1r2).
F00perfect=1q212gq+g2.
F11=1q2(1q2r4)2[(1+g2)(1q2r2)2gqt2]3×{qt2{qr2[(gq)2+(1gq)2](3+q2r4)+2(gq)(1gq)(1+3q2r4)}[(1+g)2(1q2r2)2gqt2]+q2t4(1+q2r4)[(1+g2)(1q2r2)2gqt2]2+2[1gq+qr2(gq)]2[gq+qr2(1gq)]2},
F11perfect=1q2(12gq+g2)3[(gq)2(1gq)2+g2(1q2)2].
Fqubit=F00F11.
EN(ρ)=max{0,ln[ν˜(ρ)]},
ν˜(ρ)=(1R)cosh(2artanhq)+R(1R)sinh(2artanhq),
Fq=g1(R)=1+R2(1+R)4.
Rclassic0.11.
n,m=0k,l=0min(n,m)(nk)(ml)(n+mklmk)AnBmCkDl.
A=B=gqt21+g2,C=(rt)2(1+g2),D=Bg2.
1π0dyCd2xeyeB(y+ACx)(y+ADx*)eAy(x+x*)e|x|2,
11ABA2CB2DABCD.
F11=(1q2)(1+g2)πg20dyCd2x[f(x,x*,y)×eyeA(y+ABx)(y+ACx*)eAy(x+x*)e|x|2],
f(x,x*,y)=A(Axy1+g2)(Ax*g2y1+g2)+[A(y+ABx)y1+g2]×[A(y+ABg2x*)g2y1+g2]×(Axy1+g2)(Ax*g2y1+g2).
1πCd2x  xnx*mexp(a|x|2+b1x+b2x*)=1anb1nmb2mb2exp(b1b2a).
|H=|1H|0V
|S=cH|H+cV|V,
cH2+cV2=1,
U^(aH1V)U^=aS1P,U^(1HaV)U^=1SaP.
U^(aH1V)U^=aS1P,U^(1HaV)U^=1SaP.
Fqubit=kl,mnd2βHd2βV|H|U^T^kl,mn(βH,βV)U^|H|2,
1q2π(rta^)kk!(t2q)n^(rta^)ll!,
T^kl(β)=[rt(a^+gβ)]kk![rtq(a^+gβ*)]ll!T^t2qg(β).
Fqubit=d2βHd2βVH|Uert[EH(gβH)+EV(gβV)]ertq[EH+(gβH)+EV+(gβV)]Tt2qg(βH,βV)U(|HH|)|H,
βS=cHβH+cVβV,βP=cVβHcHβV.
Uea[EH±(βH)+EV±(βV)]U=ea[EH±(βS)+EV±(βP)].
U[EH±(βH)+EV±(βV)]U=[EH±(βS)+EV±(βP)],
{U[EH+(βH)+EV+(βV)]U}(ρ)=U[(a^H+βH*)Uρ  U(a^H+βH)+(a^V+βV*)Uρ  U(a^V+βV)]U=(cHa^H+cVa^V+βH*)ρ(cHa^H+cVa^V+βH)+(cVa^HcHa^V+βV*)ρ(cVa^HcHa^V+βV)=(a^H+cHβH*+cVβV*)ρ(a^H+cHβH+cVβV)+(a^V+cVβH*cHβV*)ρ(a^V+cVβHcHβV)=[EH+(βS)+EV+(βP)](ρ),
Fqubit=d2βHd2βVH|ert[EH(gβS)+EV(gβP)]ertq[EH+(gβS)+EV+(gβP)]Tt2qg(βS,βP)(|HH|)|H.