Abstract

Three different quantifiers, entanglement of formation (ENT), quantum discord (QD), and measurement-induced disturbance (MID), are used to measure the quantum correlations of two qubits in a common squeezed bath. A subspace was found for initial conditions in a squeezed bath, where the system experiences no decoherence. We relate the three measurements with the “distance” from the initial condition to the decoherence free subspace, in order to study the effect of the decoherence in the quantum correlations. We show examples of a system with quantum correlations even when entanglement is null. Furthermore, we study the necessary conditions for the system to become truly classical. We found that, under certain initial conditions and at specific times, the system becomes classical and both the QD and the MID vanish, thus observing the phenomena of sudden death and revival of the quantum correlations. Finally, we observe discontinuities in the QD.

© 2012 Optical Society of America

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  1. W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715–775 (2003).
    [CrossRef]
  2. M. Orszag, Quantum Optics (Springer, 2000).
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    [CrossRef]
  4. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [CrossRef]
  5. A. K. Ekert, “Quantum privacy amplification and security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 67, 661–663 (1991).
    [CrossRef]
  6. D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
    [CrossRef]
  7. C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
    [CrossRef]
  8. M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
    [CrossRef]
  9. J. Niset and N. Cerf, “Multiparticle non-locality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
    [CrossRef]
  10. S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
    [CrossRef]
  11. D. A. Meyer, “Sophisticated quantum search without entanglement,” Phys. Rev. Lett. 85, 2014–2017 (2000).
    [CrossRef]
  12. A. Datta and G. Vidal, “Role of entanglement and correlations in mixed-state quantum computing,” Phys. Rev. A 75, 042310 (2007).
    [CrossRef]
  13. H. Ollivier, and W. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
    [CrossRef]
  14. L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
    [CrossRef]
  15. S. Luo, “Using measurement induced disturbance to characterize correlations as classical or quantum,” Phys. Rev. A 77, 022301 (2008).
    [CrossRef]
  16. D. Mundarain and M. Orszag, “Decoherence-free subspace and entanglement by interaction with a common squeezed bath,” Phys. Rev. A 75, 040303(R) (2007).
    [CrossRef]
  17. D. A. Lidar and K. B. Whaley, “Decoherence-free subspaces and subsystems,” in Irreversible Quantum Dynamics, Vol. 622 of Lecture Notes in Physics (Springer, 2003), pp. 83–120.
  18. M. Hernandez and M. Orszag, “Decoherence and disentanglement for two qubits in a common squeezed reservoir,” Phys. Rev. A 78, 042114 (2008).
    [CrossRef]
  19. C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
    [CrossRef]
  20. S. Hill and W. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
    [CrossRef]
  21. W. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248(1998).
    [CrossRef]
  22. L. Wang, J. Huang, and S. Y. Zhu, “A new criteria for zero quantum discord,” New J. Phys. 13, 06345 (2011).
  23. D. Mundarain, M. Orszag, and J. Stephany, “Total quantum Zeno effect and intelligent states for a two-level system in a squeezed bath,” Phys. Rev. A 74, 052107 (2006).
    [CrossRef]
  24. M. Ikram, F. Li, and M. Zubairy, “Disentanglement in a two-qubit system subjected to dissipation environments,” Phys. Rev. A 75, 062336 (2007).
    [CrossRef]
  25. S. Luo, “Quantum discord for two-qubit systems,” Phys. Rev. A 77, 042303 (2008).
    [CrossRef]
  26. M. Ali, A. R. P. Rau, and G. Alber, “Quantum discord for two-qubit X states,” Phys. Rev. A 81, 042105 (2010).
    [CrossRef]
  27. M. Ali, A. R. P. Rau, and G. Alber, “Erratum: quantum discord for two-qubit X states,” Phys. Rev. A 82, 069902(E) (2010).
  28. B. Dakic, V. Vedral, and C. Brukner, “Necessary and sufficient condition for non-zero quantum discord,” Phys. Rev. Lett. 105, 190502 (2010).
    [CrossRef]
  29. R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

2011 (1)

L. Wang, J. Huang, and S. Y. Zhu, “A new criteria for zero quantum discord,” New J. Phys. 13, 06345 (2011).

2010 (4)

M. Ali, A. R. P. Rau, and G. Alber, “Quantum discord for two-qubit X states,” Phys. Rev. A 81, 042105 (2010).
[CrossRef]

M. Ali, A. R. P. Rau, and G. Alber, “Erratum: quantum discord for two-qubit X states,” Phys. Rev. A 82, 069902(E) (2010).

B. Dakic, V. Vedral, and C. Brukner, “Necessary and sufficient condition for non-zero quantum discord,” Phys. Rev. Lett. 105, 190502 (2010).
[CrossRef]

M. Orszag and M. Hernandez, “Coherence and entanglement in a two-qubit system,” Adv. Opt. Photon. 2, 229–286 (2010).
[CrossRef]

2008 (3)

S. Luo, “Using measurement induced disturbance to characterize correlations as classical or quantum,” Phys. Rev. A 77, 022301 (2008).
[CrossRef]

M. Hernandez and M. Orszag, “Decoherence and disentanglement for two qubits in a common squeezed reservoir,” Phys. Rev. A 78, 042114 (2008).
[CrossRef]

S. Luo, “Quantum discord for two-qubit systems,” Phys. Rev. A 77, 042303 (2008).
[CrossRef]

2007 (3)

M. Ikram, F. Li, and M. Zubairy, “Disentanglement in a two-qubit system subjected to dissipation environments,” Phys. Rev. A 75, 062336 (2007).
[CrossRef]

D. Mundarain and M. Orszag, “Decoherence-free subspace and entanglement by interaction with a common squeezed bath,” Phys. Rev. A 75, 040303(R) (2007).
[CrossRef]

A. Datta and G. Vidal, “Role of entanglement and correlations in mixed-state quantum computing,” Phys. Rev. A 75, 042310 (2007).
[CrossRef]

2006 (2)

J. Niset and N. Cerf, “Multiparticle non-locality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[CrossRef]

D. Mundarain, M. Orszag, and J. Stephany, “Total quantum Zeno effect and intelligent states for a two-level system in a squeezed bath,” Phys. Rev. A 74, 052107 (2006).
[CrossRef]

2005 (1)

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

2003 (1)

W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715–775 (2003).
[CrossRef]

2001 (2)

H. Ollivier, and W. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[CrossRef]

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[CrossRef]

2000 (1)

D. A. Meyer, “Sophisticated quantum search without entanglement,” Phys. Rev. Lett. 85, 2014–2017 (2000).
[CrossRef]

1999 (2)

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

1998 (1)

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

1997 (1)

S. Hill and W. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
[CrossRef]

1996 (2)

C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

1993 (1)

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

1991 (1)

A. K. Ekert, “Quantum privacy amplification and security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

Alber, G.

M. Ali, A. R. P. Rau, and G. Alber, “Quantum discord for two-qubit X states,” Phys. Rev. A 81, 042105 (2010).
[CrossRef]

M. Ali, A. R. P. Rau, and G. Alber, “Erratum: quantum discord for two-qubit X states,” Phys. Rev. A 82, 069902(E) (2010).

Ali, M.

M. Ali, A. R. P. Rau, and G. Alber, “Erratum: quantum discord for two-qubit X states,” Phys. Rev. A 82, 069902(E) (2010).

M. Ali, A. R. P. Rau, and G. Alber, “Quantum discord for two-qubit X states,” Phys. Rev. A 81, 042105 (2010).
[CrossRef]

Auccaise, R.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Bennett, C.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

Bennett, C. H.

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

Bonagamba, T. J.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Brassard, G.

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

Braunstein, S. L.

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

Brukner, C.

B. Dakic, V. Vedral, and C. Brukner, “Necessary and sufficient condition for non-zero quantum discord,” Phys. Rev. Lett. 105, 190502 (2010).
[CrossRef]

Caves, C. M.

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

Celeri, L. C.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Cerf, N.

J. Niset and N. Cerf, “Multiparticle non-locality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[CrossRef]

Crepeau, C.

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

Dakic, B.

B. Dakic, V. Vedral, and C. Brukner, “Necessary and sufficient condition for non-zero quantum discord,” Phys. Rev. Lett. 105, 190502 (2010).
[CrossRef]

Datta, A.

A. Datta and G. Vidal, “Role of entanglement and correlations in mixed-state quantum computing,” Phys. Rev. A 75, 042310 (2007).
[CrossRef]

deAzevedo, E. R.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Deutsch, D.

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

DiVicenzo, D.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

Ekert, A. K.

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

A. K. Ekert, “Quantum privacy amplification and security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

Fuchs, C.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

Henderson, L.

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[CrossRef]

Hernandez, M.

M. Orszag and M. Hernandez, “Coherence and entanglement in a two-qubit system,” Adv. Opt. Photon. 2, 229–286 (2010).
[CrossRef]

M. Hernandez and M. Orszag, “Decoherence and disentanglement for two qubits in a common squeezed reservoir,” Phys. Rev. A 78, 042114 (2008).
[CrossRef]

Hill, S.

S. Hill and W. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
[CrossRef]

Horodecki, M.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Horodecki, P.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Horodecki, R.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Huang, J.

L. Wang, J. Huang, and S. Y. Zhu, “A new criteria for zero quantum discord,” New J. Phys. 13, 06345 (2011).

Ikram, M.

M. Ikram, F. Li, and M. Zubairy, “Disentanglement in a two-qubit system subjected to dissipation environments,” Phys. Rev. A 75, 062336 (2007).
[CrossRef]

Jozsa, R.

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

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

Li, F.

M. Ikram, F. Li, and M. Zubairy, “Disentanglement in a two-qubit system subjected to dissipation environments,” Phys. Rev. A 75, 062336 (2007).
[CrossRef]

Lidar, D. A.

D. A. Lidar and K. B. Whaley, “Decoherence-free subspaces and subsystems,” in Irreversible Quantum Dynamics, Vol. 622 of Lecture Notes in Physics (Springer, 2003), pp. 83–120.

Linden, N.

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

Luo, S.

S. Luo, “Using measurement induced disturbance to characterize correlations as classical or quantum,” Phys. Rev. A 77, 022301 (2008).
[CrossRef]

S. Luo, “Quantum discord for two-qubit systems,” Phys. Rev. A 77, 042303 (2008).
[CrossRef]

Macchiavello, C.

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

Maziero, J.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Meyer, D. A.

D. A. Meyer, “Sophisticated quantum search without entanglement,” Phys. Rev. Lett. 85, 2014–2017 (2000).
[CrossRef]

Mor, T.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

Mundarain, D.

D. Mundarain and M. Orszag, “Decoherence-free subspace and entanglement by interaction with a common squeezed bath,” Phys. Rev. A 75, 040303(R) (2007).
[CrossRef]

D. Mundarain, M. Orszag, and J. Stephany, “Total quantum Zeno effect and intelligent states for a two-level system in a squeezed bath,” Phys. Rev. A 74, 052107 (2006).
[CrossRef]

Niset, J.

J. Niset and N. Cerf, “Multiparticle non-locality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[CrossRef]

Oliveira, I. S.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Ollivier, H.

H. Ollivier, and W. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[CrossRef]

Oppenheim, J.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Orszag, M.

M. Orszag and M. Hernandez, “Coherence and entanglement in a two-qubit system,” Adv. Opt. Photon. 2, 229–286 (2010).
[CrossRef]

M. Hernandez and M. Orszag, “Decoherence and disentanglement for two qubits in a common squeezed reservoir,” Phys. Rev. A 78, 042114 (2008).
[CrossRef]

D. Mundarain and M. Orszag, “Decoherence-free subspace and entanglement by interaction with a common squeezed bath,” Phys. Rev. A 75, 040303(R) (2007).
[CrossRef]

D. Mundarain, M. Orszag, and J. Stephany, “Total quantum Zeno effect and intelligent states for a two-level system in a squeezed bath,” Phys. Rev. A 74, 052107 (2006).
[CrossRef]

M. Orszag, Quantum Optics (Springer, 2000).

Peres, A.

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

Popescu, S.

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

Rains, E.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

Rau, A. R. P.

M. Ali, A. R. P. Rau, and G. Alber, “Quantum discord for two-qubit X states,” Phys. Rev. A 81, 042105 (2010).
[CrossRef]

M. Ali, A. R. P. Rau, and G. Alber, “Erratum: quantum discord for two-qubit X states,” Phys. Rev. A 82, 069902(E) (2010).

Sanpera, A.

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

Sarthour, R. S.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Schack, R.

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

Sen, A.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Sen, U.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Serra, R. M.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Shor, P.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

Smolin, J.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

Soares-Pinto, D. O.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Souza, A. M.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

Stephany, J.

D. Mundarain, M. Orszag, and J. Stephany, “Total quantum Zeno effect and intelligent states for a two-level system in a squeezed bath,” Phys. Rev. A 74, 052107 (2006).
[CrossRef]

Synak-Radtke, B.

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

Vedral, V.

B. Dakic, V. Vedral, and C. Brukner, “Necessary and sufficient condition for non-zero quantum discord,” Phys. Rev. Lett. 105, 190502 (2010).
[CrossRef]

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[CrossRef]

Vidal, G.

A. Datta and G. Vidal, “Role of entanglement and correlations in mixed-state quantum computing,” Phys. Rev. A 75, 042310 (2007).
[CrossRef]

Wang, L.

L. Wang, J. Huang, and S. Y. Zhu, “A new criteria for zero quantum discord,” New J. Phys. 13, 06345 (2011).

Whaley, K. B.

D. A. Lidar and K. B. Whaley, “Decoherence-free subspaces and subsystems,” in Irreversible Quantum Dynamics, Vol. 622 of Lecture Notes in Physics (Springer, 2003), pp. 83–120.

Wootters, W.

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

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

S. Hill and W. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
[CrossRef]

C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

Wootters, W. K.

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

Zhu, S. Y.

L. Wang, J. Huang, and S. Y. Zhu, “A new criteria for zero quantum discord,” New J. Phys. 13, 06345 (2011).

Zubairy, M.

M. Ikram, F. Li, and M. Zubairy, “Disentanglement in a two-qubit system subjected to dissipation environments,” Phys. Rev. A 75, 062336 (2007).
[CrossRef]

Zurek, W.

H. Ollivier, and W. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[CrossRef]

Zurek, W. H.

W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715–775 (2003).
[CrossRef]

Adv. Opt. Photon. (1)

J. Phys. A (1)

L. Henderson and V. Vedral, “Classical, quantum and total correlations,” J. Phys. A 34, 6899–6905 (2001).
[CrossRef]

New J. Phys. (1)

L. Wang, J. Huang, and S. Y. Zhu, “A new criteria for zero quantum discord,” New J. Phys. 13, 06345 (2011).

Phys. Rev. A (13)

D. Mundarain, M. Orszag, and J. Stephany, “Total quantum Zeno effect and intelligent states for a two-level system in a squeezed bath,” Phys. Rev. A 74, 052107 (2006).
[CrossRef]

M. Ikram, F. Li, and M. Zubairy, “Disentanglement in a two-qubit system subjected to dissipation environments,” Phys. Rev. A 75, 062336 (2007).
[CrossRef]

S. Luo, “Quantum discord for two-qubit systems,” Phys. Rev. A 77, 042303 (2008).
[CrossRef]

M. Ali, A. R. P. Rau, and G. Alber, “Quantum discord for two-qubit X states,” Phys. Rev. A 81, 042105 (2010).
[CrossRef]

M. Ali, A. R. P. Rau, and G. Alber, “Erratum: quantum discord for two-qubit X states,” Phys. Rev. A 82, 069902(E) (2010).

M. Hernandez and M. Orszag, “Decoherence and disentanglement for two qubits in a common squeezed reservoir,” Phys. Rev. A 78, 042114 (2008).
[CrossRef]

C. Bennett, D. DiVicenzo, J. Smolin, and W. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996).
[CrossRef]

S. Luo, “Using measurement induced disturbance to characterize correlations as classical or quantum,” Phys. Rev. A 77, 022301 (2008).
[CrossRef]

D. Mundarain and M. Orszag, “Decoherence-free subspace and entanglement by interaction with a common squeezed bath,” Phys. Rev. A 75, 040303(R) (2007).
[CrossRef]

A. Datta and G. Vidal, “Role of entanglement and correlations in mixed-state quantum computing,” Phys. Rev. A 75, 042310 (2007).
[CrossRef]

C. Bennett, D. DiVicenzo, C. Fuchs, T. Mor, E. Rains, P. Shor, J. Smolin, and W. Wootters, “Quantum non-locality without entanglement,” Phys. Rev. A 59, 1070–1091 (1999).
[CrossRef]

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, and B. Synak-Radtke, “Local versus non-localinformation in quantum information theory: formalism and phenomena,” Phys. Rev. A 71, 062307 (2005).
[CrossRef]

J. Niset and N. Cerf, “Multiparticle non-locality without entanglement in many dimensions,” Phys. Rev. A 74, 052103 (2006).
[CrossRef]

Phys. Rev. Lett. (9)

S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, “Separability of very noisy mixed states and implications for NMR quantum computing,” Phys. Rev. Lett. 83, 1054–1057 (1999).
[CrossRef]

D. A. Meyer, “Sophisticated quantum search without entanglement,” Phys. Rev. Lett. 85, 2014–2017 (2000).
[CrossRef]

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

A. K. Ekert, “Quantum privacy amplification and security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

D. Deutsch, A. K. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996).
[CrossRef]

H. Ollivier, and W. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2001).
[CrossRef]

S. Hill and W. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. 78, 5022–5025 (1997).
[CrossRef]

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

B. Dakic, V. Vedral, and C. Brukner, “Necessary and sufficient condition for non-zero quantum discord,” Phys. Rev. Lett. 105, 190502 (2010).
[CrossRef]

Rev. Mod. Phys. (1)

W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715–775 (2003).
[CrossRef]

Other (3)

M. Orszag, Quantum Optics (Springer, 2000).

D. A. Lidar and K. B. Whaley, “Decoherence-free subspaces and subsystems,” in Irreversible Quantum Dynamics, Vol. 622 of Lecture Notes in Physics (Springer, 2003), pp. 83–120.

R. Auccaise, L. C. Celeri, D. O. Soares-Pinto, E. R. deAzevedo, J. Maziero, A. M. Souza, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, “Environment induced sudden transition in quantum discord dynamics,” Phys. Rev. Lett.107, 140403 (2011).

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Figures (7)

Fig. 1.
Fig. 1.

All the possible time evolutions for QD. (a) Birth of QD, (b) simultaneous death and revival of QD, (c) asymptotic death of QD, (d) several points of death and revival of QD, (e) QD never vanishes, and (f) zero QD. The same evolutions are possible for MID, but we must replace the inside region by classical states.

Fig. 2.
Fig. 2.

Quantum correlations for initial condition |Ψ1 in squeezed reservoir. (a) Entanglement for the initial condition |Ψ1, with N=0.1, and different values of ϵ: ϵ=0.0001 (dotted–dashed), ϵ=0.2 (long dashed), ϵ=0.5 (solid), ϵ=0.7 (dotted), and ϵ=0.8 (dashed). (b) QD for the initial condition |Ψ1, with N=0.1, and different values of ϵ: ϵ=0.0001 (dotted–dashed), ϵ=0.2 (long dashed), ϵ=0.5 (solid), ϵ=0.7 (dotted), and ϵ=0.8 (dashed). (c) MID for the initial condition |Ψ1, with N=0.1, and different values of ϵ: ϵ=0.0001 (dotted–dashed), ϵ=0.2 (long dashed), ϵ=0.5 (solid), ϵ=0.7 (dotted), and ϵ=0.8 (dashed).

Fig. 3.
Fig. 3.

Quantum correlations for initial condition |Ψ2 in a squeezed reservoir. (a) Entanglement for the initial condition |Ψ2, with N=0.1, and different values of ϵ: ϵ=0.0001 (dotted–dashed), ϵ=0.369192 (solid), ϵ=0.6 (long dashed), ϵ=1/2 (dotted), and ϵ=0.9 (dashed). (b) QD for the initial condition |Ψ2, with N=0.1, and different values of ϵ: ϵ=0.0001 (dotted–dashed), ϵ=0.369192 (solid), ϵ=0.6 (long dashed), ϵ=1/2 (dotted), and ϵ=0.9 (dashed). (c) MID for the initial condition |Ψ2, with N=0.1, and different values of ϵ: ϵ=0.0001 (dotted–dashed), ϵ=0.369192 (solid), ϵ=0.6 (long dashed), ϵ=1/2 (dotted), and ϵ=0.9 (dashed).

Fig. 4.
Fig. 4.

Quantum correlations for the initial condition |Ψ2 with ϵ=0.369192 and N=0.1. Entanglement (dashed), QD (solid), and MID (dotted).

Fig. 5.
Fig. 5.

The points are the zeros of QD and MID; each of them corresponds to a different value of ϵ.

Fig. 6.
Fig. 6.

Quantum correlations for the initial condition |Ψ2 in a vacuum reservoir (N=0), for ϵ=0.4, entanglement (dotted–dashed), QD (solid), and MID (dashed). The inner plot represents the point where the quantum correlations are zero as we vary ϵ.

Fig. 7.
Fig. 7.

Coherences ρ14 and ρ23 for the initial condition |Ψ2, with N=0.1, and different values of ϵ: ρ23, ϵ=0.0001 (dotted–dashed), ρ23, ϵ=0.369192 (long dashed), ρ23, ϵ=0.6 (dashed), ρ23, ϵ=0.9 (dotted), ρ14, and ϵ=0.9 (solid).

Equations (27)

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C(ρ)=max{0,λ1λ2λ3λ4},
ρ=ipiρiAρiB,
Q(ρ)=I(ρ)C(ρ).
ρ=ikpikρiAΠkB,
ρ(iAjA)=iA|ρAB|jA=k=1Ml=1MiAkB|ρAB|jAlB|kBlB|,
ρ14=ρ23,ρ12(ρ13ρ24)=ρ23(ρ11ρ22),ρ34(ρ13ρ24)=ρ23(ρ33ρ44).
M(ρ)=minΠ{I(ρ)I(Π(ρ))},
ρ=ijpijΠiAΠjB,
I(ρ)=2S,C(ρ)=S,Q(ρ)=S,M(ρ)=S,
ρ^t=γ2i,j=12[(N+1)(2σiρ^σjσiσjρ^ρ^σiσj)+N(2σiρ^σjσiσjρ^ρ^σiσj)M(2σiρ^σjσiσjρ^ρ^σiσj)M*(2σiρ^σjσiσjρ^ρ^σiσj)],
ρt=12γ(2SρSSSρρSS),
S=N+1(σ1+σ2)NeiΨ(σ1+σ2)=cosh(r)(σ1+σ2)sinh(r)eiΨ(σ1+σ2),
|ϕ1=1N2+M2(N|+++MeiΨ|),
|ϕ2=12(|+|+).
|ϕ3=12(|++|+),
|ϕ4=1N2+M2(M|++NeiΨ|).
|Ψ1=ϵ|ϕ1+1ϵ2|ϕ4,
|Ψ2=ϵ|ϕ2+1ϵ2|ϕ3,
(ρ1100ρ140ρ22ρ2300ρ32ρ330ρ4100ρ44).
C(ρ)=max{0,C1(ρ),C2(ρ)},
C1(ρ)=2(ρ23ρ32ρ11ρ44),
C2(ρ)=2(ρ14ρ41ρ22ρ33),
min{Bk}Q=min{Bk}{Q1,Q2,Q3},
Q1=S(ρB)S(ρAB)+ρ11logρ11ρ11+ρ33ρ33logρ33ρ11+ρ33ρ22logρ22ρ22+ρ44ρ44logρ44ρ22+ρ44,Q2,3=S(ρB)S(ρAB)+112(1Γ2+4Θ2,3)log(1Γ2+4Θ2,3)12(1+Γ2+4Θ2,3)log(1+Γ2+4Θ2,3),
M(ρ)=S(ρAB)+iρiilogρii.
α=N1+2N,β=1+11N+24N2+12N3(1+2N)(1+12N+12N2).
S=β2log2β2α2log2α2,

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