Abstract

When two entangled qubits, each owned by Alice and Bob, undergo separate decoherence, the amount of entanglement is reduced, and often, weak decoherence causes complete loss of entanglement, known as entanglement sudden death. Here we show that it is possible to apply quantum measurement reversal on a single-qubit to avoid entanglement sudden death, rather than on both qubits. Our scheme has important applications in quantum information processing protocols based on distributed or stored entangled qubits as they are subject to decoherence.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  11. S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
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    [CrossRef]
  14. L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  26. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
    [CrossRef] [PubMed]
  27. P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
    [CrossRef]
  28. J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
    [CrossRef]
  29. J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
    [CrossRef] [PubMed]
  30. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [CrossRef]
  31. Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
    [CrossRef] [PubMed]

2013 (1)

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

2012 (1)

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

2011 (1)

2010 (2)

Q. Sun, M. Al-Amri, L. Davidovich, and M. S. Zubairy, “Reversing entanglement change by a weak measurement,” Phys. Rev. A 82, 052323 (2010).
[CrossRef]

A. N. Korotkov and K. Keane, “Decoherence suppression by quantum measurement reversal,” Phys. Rev. A 81, 040103(R) (2010).
[CrossRef]

2009 (2)

Y.-S. Kim, Y.-W. Cho, Y.-S. Ra, and Y.-H. Kim, “Reversing the weak quantum measurement for a photonic qubit,” Opt. Express 17, 11978–11985 (2009).
[CrossRef] [PubMed]

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Reversing the weak measurement of an arbitrary field with finite photon number,” Phys. Rev. A 80, 033838 (2009).
[CrossRef]

2008 (4)

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

J. G. Oliveira, R. Rossi, and M. C. Nemes, “Protecting, enhancing, and reviving entanglement,” Phys. Rev. A 78, 044301 (2008).
[CrossRef]

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

2007 (1)

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

2006 (1)

A. N. Korotkov and A. N. Jordan, “Undoing weak quantum measurement of a solid-state qubit,” Phys. Rev. Lett. 97, 166805 (2006).
[CrossRef]

2004 (2)

P. Facchi, D. A. Lidar, and S. Pascazio, “Unification of dynamical decoupling and the quantum Zeno effect,” Phys. Rev. A 69, 032314 (2004).
[CrossRef]

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2001 (4)

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
[CrossRef]

J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[CrossRef]

2000 (2)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[CrossRef]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

1999 (1)

M. Koashi and M. Ueda, “Reversing measurement and probabilistic quantum Error correction,” Phys. Rev. Lett. 82, 2598–2601 (1999).
[CrossRef]

1998 (2)

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

1997 (1)

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

1996 (2)

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

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] [PubMed]

1988 (1)

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

Al-Amri, M.

Q. Sun, M. Al-Amri, L. Davidovich, and M. S. Zubairy, “Reversing entanglement change by a weak measurement,” Phys. Rev. A 82, 052323 (2010).
[CrossRef]

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Reversing the weak measurement of an arbitrary field with finite photon number,” Phys. Rev. A 80, 033838 (2009).
[CrossRef]

Alley, C. O.

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

Almeida, M. P.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

Altepeter, J. B.

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Ansmann, M.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Barraza-Lopez, S.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
[CrossRef]

Bennett, C. H.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[CrossRef]

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

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] [PubMed]

Berglund, A. J.

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef] [PubMed]

Bialczak, R. C.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Bouwmeester, D.

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

Brassard, G.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

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] [PubMed]

Brukner, C.

J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[CrossRef]

Cho, Y.-W.

Chow, J. M.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Chuang, I. L.

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, Cambridge, 2000).

Cleland, A. N.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Cory, D. G.

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

Cramer, J.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

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] [PubMed]

Davidovich, L.

Q. Sun, M. Al-Amri, L. Davidovich, and M. S. Zubairy, “Reversing entanglement change by a weak measurement,” Phys. Rev. A 82, 052323 (2010).
[CrossRef]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

de Groot, P. C.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

de Melo, F.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

Devoret, M. H.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

DiCarlo, L.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

DiVincenzo, D. P.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[CrossRef]

Eberly, J. H.

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

Eibl, M.

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

Facchi, P.

P. Facchi, D. A. Lidar, and S. Pascazio, “Unification of dynamical decoupling and the quantum Zeno effect,” Phys. Rev. A 69, 032314 (2004).
[CrossRef]

Fortunato, E. M.

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

Francica, F.

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

Frunzio, L.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Gambetta, J. M.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Girvin, S. M.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
[CrossRef]

Groen, J. P.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

Gullo, N. L.

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

Hofheinz, M.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Hor-Meyll, M.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

Houck, A. A.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Itano, W. M.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Jeong, Y.-C.

Johansson, G.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

Johnson, B. R.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Jordan, A. N.

A. N. Korotkov and A. N. Jordan, “Undoing weak quantum measurement of a solid-state qubit,” Phys. Rev. Lett. 97, 166805 (2006).
[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] [PubMed]

Katz, N.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Keane, K.

A. N. Korotkov and K. Keane, “Decoherence suppression by quantum measurement reversal,” Phys. Rev. A 81, 040103(R) (2010).
[CrossRef]

Kielpinski, D.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Kim, Y.-H.

Kim, Y.-S.

Knill, E.

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

Koashi, M.

M. Koashi and M. Ueda, “Reversing measurement and probabilistic quantum Error correction,” Phys. Rev. Lett. 82, 2598–2601 (1999).
[CrossRef]

Koch, Jens

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Korotkov, A. N.

A. N. Korotkov and K. Keane, “Decoherence suppression by quantum measurement reversal,” Phys. Rev. A 81, 040103(R) (2010).
[CrossRef]

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

A. N. Korotkov and A. N. Jordan, “Undoing weak quantum measurement of a solid-state qubit,” Phys. Rev. Lett. 97, 166805 (2006).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
[CrossRef]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Kwon, O.

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

Laflamme, R.

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

Lee, J.-C.

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309–16316 (2011).
[CrossRef] [PubMed]

Lidar, D. A.

P. Facchi, D. A. Lidar, and S. Pascazio, “Unification of dynamical decoupling and the quantum Zeno effect,” Phys. Rev. A 69, 032314 (2004).
[CrossRef]

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

Lucero, E.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Majer, J.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Maniscalco, S.

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

Martinis, J. M.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Mattle, K.

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

Meyer, V.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Monroe, C.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Neeley, M.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Nemes, M. C.

J. G. Oliveira, R. Rossi, and M. C. Nemes, “Protecting, enhancing, and reviving entanglement,” Phys. Rev. A 78, 044301 (2008).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, Cambridge, 2000).

O’Connell, A.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Oliveira, J. G.

J. G. Oliveira, R. Rossi, and M. C. Nemes, “Protecting, enhancing, and reviving entanglement,” Phys. Rev. A 78, 044301 (2008).
[CrossRef]

Pan, J.-W.

J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[CrossRef]

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

Pascazio, S.

P. Facchi, D. A. Lidar, and S. Pascazio, “Unification of dynamical decoupling and the quantum Zeno effect,” Phys. Rev. A 69, 032314 (2004).
[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] [PubMed]

Picot, T.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

Plastina, F.

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

Popescu, S.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

Pravia, M. A.

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

Ra, Y.-S.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Ristè, D.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

Rossi, R.

J. G. Oliveira, R. Rossi, and M. C. Nemes, “Protecting, enhancing, and reviving entanglement,” Phys. Rev. A 78, 044301 (2008).
[CrossRef]

Rowe, M. A.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Sackett, C. A.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Salles, A.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

Schoelkopf, R. J.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Schreier, J. A.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Schumacher, B.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef] [PubMed]

Schuster, D. I.

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Shih, Y. H.

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

Simon, C.

J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[CrossRef]

Smolin, J. A.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

Souto Ribeiro, P. H.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

Stefanov, A.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
[CrossRef]

Sun, Q.

Q. Sun, M. Al-Amri, L. Davidovich, and M. S. Zubairy, “Reversing entanglement change by a weak measurement,” Phys. Rev. A 82, 052323 (2010).
[CrossRef]

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Reversing the weak measurement of an arbitrary field with finite photon number,” Phys. Rev. A 80, 033838 (2009).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Tornberg, L.

J. P. Groen, D. Ristè, L. Tornberg, J. Cramer, P. C. de Groot, T. Picot, G. Johansson, and L. DiCarlo, “Partial-measurement backaction and nonclassical weak values in a superconducting circuit,” Phys. Rev. Lett. 111, 090506 (2013).
[CrossRef] [PubMed]

Ueda, M.

M. Koashi and M. Ueda, “Reversing measurement and probabilistic quantum Error correction,” Phys. Rev. Lett. 82, 2598–2601 (1999).
[CrossRef]

Viola, L.

L. Viola, E. M. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, “Experimental realization of noiseless subsystems for quantum information processing,” Science 293, 2059–2063 (2001).
[CrossRef] [PubMed]

Walborn, S. P.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef] [PubMed]

Wang, H.

N. Katz, M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, J. M. Martinis, and A. N. Korotkov, “Reversal of the weak measurement of a quantum state in a super-conducting phase qubit,” Phys. Rev. Lett. 101, 200401 (2008).
[CrossRef]

Weinfurter, H.

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

Whaley, K. B.

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

White, A. G.

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Wineland, D. J.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[CrossRef] [PubMed]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996).
[CrossRef] [PubMed]

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] [PubMed]

Yu, T.

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

Zaffino, R. L.

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Zeilinger, A.

J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[CrossRef]

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

Zubairy, M. S.

Q. Sun, M. Al-Amri, L. Davidovich, and M. S. Zubairy, “Reversing entanglement change by a weak measurement,” Phys. Rev. A 82, 052323 (2010).
[CrossRef]

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Reversing the weak measurement of an arbitrary field with finite photon number,” Phys. Rev. A 80, 033838 (2009).
[CrossRef]

Nature (London) (4)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[CrossRef]

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

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature (London) 409, 1014–1017 (2001).
[CrossRef]

J.-W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature (London) 410, 1067–1070 (2001).
[CrossRef]

Nature Phys. (1)

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nature Phys. 8, 117–120 (2012).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (6)

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[CrossRef] [PubMed]

A. N. Korotkov and K. Keane, “Decoherence suppression by quantum measurement reversal,” Phys. Rev. A 81, 040103(R) (2010).
[CrossRef]

Q. Sun, M. Al-Amri, and M. S. Zubairy, “Reversing the weak measurement of an arbitrary field with finite photon number,” Phys. Rev. A 80, 033838 (2009).
[CrossRef]

Q. Sun, M. Al-Amri, L. Davidovich, and M. S. Zubairy, “Reversing entanglement change by a weak measurement,” Phys. Rev. A 82, 052323 (2010).
[CrossRef]

J. G. Oliveira, R. Rossi, and M. C. Nemes, “Protecting, enhancing, and reviving entanglement,” Phys. Rev. A 78, 044301 (2008).
[CrossRef]

P. Facchi, D. A. Lidar, and S. Pascazio, “Unification of dynamical decoupling and the quantum Zeno effect,” Phys. Rev. A 69, 032314 (2004).
[CrossRef]

Phys. Rev. B (1)

J. A. Schreier, A. A. Houck, Jens Koch, D. I. Schuster, B. R. Johnson, J. M. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Suppressing charge noise decoherence in superconducting charge qubits,” Phys. Rev. B 77, 180502(R) (2008).
[CrossRef]

Phys. Rev. Lett. (11)

S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef] [PubMed]

M. Koashi and M. Ueda, “Reversing measurement and probabilistic quantum Error correction,” Phys. Rev. Lett. 82, 2598–2601 (1999).
[CrossRef]

A. N. Korotkov and A. N. Jordan, “Undoing weak quantum measurement of a solid-state qubit,” Phys. Rev. Lett. 97, 166805 (2006).
[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] [PubMed]

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[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

(a) Decoherence suppression scheme using quantum measurement reversal for a single qubit state. To suppress decoherence, a set of weak and reversing measurements are performed before and after decoherence, respectively. Note that the size of the spheres corresponds to the population fraction of each level, |0〉 and |1〉. (b) Entanglement of two-qubit states which undergo separate decoherence can be recovered if both Alice and Bob carry out quantum measurement reversal. (c) The situation we considered here: Only Alice performs single-qubit quantum measurement reversal on her subsystem. W : weak measurement, D: decoherence, R: reversing measurement, Sys: system, Env: environment.

Fig. 2
Fig. 2

(a) Alice and Bob initially share a pure entangled state |Φ〉. When both subsystems suffer from decoherence, the final state ρD loses its entanglement partially or completely. (b) To suppress decoherence, Alice performs a set of weak measurement WA (p) and reversing measurement RA (pr) before and after her subsystem undergoes decoherence, respectively. Then, the resulting state ρA becomes closer to the initial state |Φ〉, i.e. ρA is more entangled than ρD. Note that Bob is not involved in this decoherence suppression scheme.

Fig. 3
Fig. 3

Experimental setup. A set of BPs and HWPs at the state preparation part is exploited for preparing the non-maximal entangled states. Weak and reversing measurements are also implemented by BPs and 45° HWPs. The amplitude damping channel for single qubit polarization state is realized using displaced Sagnac-type interferometer and additional beam splitters [7,22,24]. IF: interference filter, HWP: half-wave plate, QWP: quarter-wave plate, BP: Brewster-angle glass plate, PBS: polarizing beam splitter, BS: beam splitter, QST: quantum state tomography.

Fig. 4
Fig. 4

(a) Concurrence CD of the resulting state ρD decreases as the strength of the decoherence (D) increases. (b) Concurrence CA (CB) of the final state ρA (ρB) in the case that only Alice (Bob) perfroms single-qubit quantum measurement reversal on her (his) qubit (DA = DB = 0.617). p is the strength of the weak measurement. Solid lines are theoretical results. Negative values corresponds to Λ D for (a), and Λ A and Λ B for (b), respectively. Note that C = 0 when Λ< 0 since C = max {0,Λ}. We evaluated the fidelity between the ideally expected state and the experimentally reconstructed state for ρA and ρB. The fidelity values for ρA (FA) and ρB (FB) are averaged from the experimental data of (b), and we obtain FA = 0.945 ± 0.024 and FB = 0.935 ± 0.028.

Fig. 5
Fig. 5

Result of the scenario in Fig. 1(a) with D = 0.617. (a) State fidelities Ffix and Fexp as functions of |α| and p. Ffix and Fexp increase as the weak measurement strength p increases. (b) Success probabilities P S fix and P S exp as functions of |α| and p. P S exp is always larger than P S fix regardless of |α| and p values. Note that F → 1 and PS → 0 as p → 1 for both cases of p r fix and p r exp .

Fig. 6
Fig. 6

Result of the scenario in Fig. 1(b) with DA = DB = 0.617. (a) State fidelities Ffix and Fexp as functions of |α| and p. The state fidelities increase as the weak measurement strength p increases. (b) Success probabilities P S fix and P S exp as functions of |α| and p. Note that PS → 0 as p → 1 for all both cases.

Fig. 7
Fig. 7

Result of the scenario in Fig. 1(c) with DA = DB = 0.617. (a) State fidelities Ffix and Fexp as functions of |α| and p. The state fidelities increase as the weak measurement strength p increases. (b) Success probabilities P S fix and P S exp as functions of |α| and p. P S fix is always larger than P S exp regardless of |α| and p values. Note that F does not approach to unity and PS → 0 as p → 1 for both cases of p r fix and p r exp .

Fig. 8
Fig. 8

Result of the scenario in Fig. 1(c) with DA = 0.617 and DB = 0. (a) State fidelities Ffix and Fexp as functions of |α| and p. (b) Success probabilities P S fix and P S exp as functions of |α| and p. P S exp is always larger than P S fix regardless of |α| and p values. Note that F → 1 and PS → 0 as p → 1 for both cases of p r fix and p r exp .

Equations (28)

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C D = max { 0 , Λ D 2 D ¯ A D ¯ B | β | ( | α | D A D B | β | ) } ,
C A = max { 0 , Λ A 2 D B | β | ( | α | D A D B p ¯ | β | ) 1 + D A p ¯ | β | 2 } ,
ρ out = 1 P S ( p ¯ r ( | α | 2 + D p ¯ | β | 2 ) p ¯ r D p ¯ α β * p ¯ r D p ¯ α * β D ¯ p ¯ | β | 2 ) ,
F = 1 p | β | 4 p r | α | 4 D p ¯ | β | 2 [ 1 + ( p r 2 ) | α | 2 ] 2 | α | 2 | β | 2 [ 1 p ¯ r D p ¯ ] 1 D p r D ¯ p r | α | 2 p ( 1 D p r ) | β | 2 .
p r max = 1 p | β | 2 D p ¯ | β | 2 + | α | 2 + ( D p ¯ + p ) ( | α | 2 | β | 2 ) 2 + 4 | α | 2 1 + D ¯ p ¯ ( | α | 2 | β | 2 ) 2 D p ¯ | β | 2 + ( | α | 2 | β | 2 ) 2 + | α | 2 D p ¯ | β | 2 + | α | 2 2 | α | 4
p r fix = 2 D + p 2 D p D + 1 D p ,
F fix = 1 + | β | 2 D p ¯ 2 | α β | 2 ( 1 1 + D p ) 1 + 2 D p ¯ | β | 2 ,
F exp = 1 + D p ¯ | α β | 2 1 + D p ¯ | β | 2 .
P S fix = D ¯ p ¯ ( 1 + 2 D p ¯ | β | 2 ) 1 + D p ¯ and P S exp = D ¯ p ¯ ( 1 + D p ¯ | β | 2 ) .
ρ out = 1 P S ( ( | α | 2 + D 2 | β | 2 p ¯ 2 ) p ¯ r 2 0 0 p ¯ D ¯ p ¯ r α β * 0 D | β | 2 D ¯ p ¯ 2 p ¯ r 0 0 0 0 D | β | 2 D ¯ p ¯ 2 p ¯ r 0 p ¯ D ¯ p ¯ r α * β 0 0 | β | 2 D ¯ 2 p ¯ 2 ) ,
F = | β | 2 D 2 p ¯ 2 [ | α | 2 ( p r 2 ) p r + 1 ] 2 | β | 2 D p ¯ [ p ¯ + | α | 2 ( p p r ) ] + [ p ¯ + | α | 2 ( p p r ) ] 2 | α | 2 D ¯ p r [ ( D + 1 ) p r 2 ] + [ | β | 2 ( p 2 ) p + 1 ] ( D p r 1 ) 2 ,
p r max = D ¯ p ¯ + 2 p | α | 2 2 | α | 2 ( 1 D p ¯ ) D ¯ p ¯ | α | 2 D p ¯ | β | 2 ( 4 | α | 2 D p ¯ ) | α | 2 + D 2 p ¯ 2 | β | 2 2 | α | 2 ( 1 + D p ¯ ) ,
p r fix = D 2 p ¯ 2 + 1 D ¯ p ¯ D 2 p ¯ 2 + 1 ,
F fix = 2 | α | 2 | β | 2 ( D 2 p ¯ 2 + 1 1 ) + D 2 p ¯ 2 | β | 2 + 1 2 D p ¯ | β | 2 ( D 2 p ¯ 2 + 1 + D p ¯ ) + 1 .
F exp = 1 + D 2 p ¯ 2 | α | 2 | β | 2 1 + D p ¯ | β | 2 ( D p ¯ + 2 ) .
P S fix = D ¯ 2 p ¯ 2 ( D 2 p ¯ 2 | β | 2 + | α | 2 D 2 p ¯ 2 + 1 + 2 D p ¯ | β | 2 D 2 p ¯ 2 + 1 + | β | 2 ) ,
P S exp = D ¯ 2 p ¯ 2 [ 1 + D p ¯ | β | 2 ( D p ¯ + 2 ) ] .
ρ out = 1 P S ( p ¯ r ( D 2 p ¯ | β | 2 + | α | 2 ) 0 0 α β * D ¯ p ¯ p r 0 D D ¯ p ¯ | β | 2 p ¯ r 0 0 0 0 D D ¯ p ¯ | β | 2 0 α * β D ¯ p ¯ p r 0 0 D ¯ 2 p ¯ | β | 2 ) ,
F = D 2 p ¯ | β | 2 ( 1 | α | 2 p r ) 2 | α | 2 ( p p r 1 ) ( D | β | 2 1 ) | α | 4 ( 2 p p r + p r 2 ) 2 D | β | 2 + ( 2 D 1 ) p | β | 4 + 1 ( p | β | 2 1 ) ( D p r 1 ) D ¯ | α | 2 p r .
p r fix = ( 2 D p ¯ + p ) [ 2 D p ¯ ( D ( 2 D p ¯ + p ) + D [ D ( ( 2 D p ¯ + p ) 2 4 p ¯ ) 4 p ] + 4 2 ) ] 2 ( D p ¯ + 1 ) 2 .
F exp = D 2 p ¯ | α | 2 | β | 2 + 2 ( D 1 ) | α | 2 | β | 2 D | β | 4 + 1 D p ¯ | β | 2 + 1 ,
P S exp = D ¯ p ¯ ( D p ¯ | β | 2 + 1 ) .
ρ out = 1 P S ( | α | 2 p ¯ r 0 0 D p ¯ p ¯ r α β * 0 D | β | 2 p ¯ p ¯ r 0 0 0 0 0 0 D p p r α * β 0 0 | β | 2 D ¯ p ¯ ) ,
F = D p ¯ | β | 4 + | α | 4 ( 2 D p ¯ p ¯ r + p r 2 ) 2 | α | 2 ( D p ¯ p ¯ r 1 ) + p | β | 4 1 D ¯ | α | 2 p r + ( p | β | 2 1 ) ( 1 D p r ) ,
p r max = D 2 p ¯ 2 | β | 4 D p ¯ | α | 2 ( | β | 2 + 1 ) + p | α | 4 ( | α | 2 D p ¯ | β | 2 ) 2 .
p r fix = D 2 p ¯ 2 3 D p ¯ + p ( D p ¯ 1 ) 2 .
F fix = ( D p ¯ | β | 2 + 1 ) 2 D p ¯ | β | 2 ( D p ¯ + 3 ) + 1 , and F exp = 1 D p ¯ | β | 2 + 1 .
P S fix = D ¯ p ¯ [ D p ¯ | β | 2 ( D p ¯ + 3 ) + 1 ] ( D p ¯ + 1 ) 2 , and P S exp = D ¯ p ¯ ( D p ¯ | β | 2 + 1 ) .

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