Abstract
In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEMS) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-birth of entanglement. On the other hand, two qubits MEMS exhibit the robust character against the phase flip, phase damping and depolarization channels. The elegant behavior of all the quantum channels have been investigated with varying parameter of quantum state MEMS in different cases.
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Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)
Meyer, D.: Quantum strategies. Phys. Rev. Lett. 82, 1052 (1999)
Lugiato, L.: Quantum imaging. J. Opt. B: Quantum Semiclass. 4, 3 (2002)
Mosca, M.: Quantum algorithms. arXiv:0808.0369 (2008)
Wittek, P.: Quantum Machine Learning: What Quantum Computing Means to Data Mining. Academic Press, Cambridge (2014)
Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)
Kimble, H.J.: The quantum internet. Nature. 453, 7198 (2008)
Gisin, N., Thew, R.: Quantum communication. Nature Photon. 1, 165 (2007)
Chen, J., et al.: Schemes for fibre-based entanglement generation in the telecom band. New J. Phys. 9, 289 (2007)
Sangouard, N., Simon, C., de Riedmatten, H, Nicolas, G.: Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33 (2011)
Brennen, G., Giacobino, E., Simon, C.: Focus on quantum memory. New J. Phys. 17, 050201 (2015)
Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)
Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 30, 598 (2009)
Sharma, K.K., Awasthi, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit–qutrit systems under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 12, 3437 (2013)
Sharma, K.K., Pandey, S.N.: Entanglement dynamics in two parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 13, 2017 (2014)
Sharma, K.K., Pandey, S.N.: Influence of Dzyaloshinshkii–Moriya interaction on quantum correlations in two qubit Werner states and MEMS. Quantum Inf. Process. 14, 1361 (2015)
Sharma, K.K., Pandey, S.N.: Dzyaloshinshkii–moriya interaction as an agent to free the bound entan- gled states. Quantum Inf. Process. 15, 1539 (2016)
Sharma, K.K., Pandey, S.N.: Dynamics of entanglement in two parameter qubit–qutrit states with x-component of DM interaction. Commun. Theor. Phys. 65, 278 (2016)
Sharma, K.K., Pandey, S.N.: Robustness of W and Greenberger Horne Zeilinger states against Dzyaloshinskii–Moriya interaction. Quant. Inf. Proc. 15, 4995 (2016)
Koashi, M., Ueda, M.: Reversing measurement and probabilistic quantum Error correction. Phys. Rev. Lett. 82, 2598 (1999)
Korotkov, A.N., Jordan, A.N.: Undoing weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)
Sun, Q., Al-Amri, M., Zubairy, M.S.: Reversing the weak measurement of an arbitrary field with finite photon number. Phys. Rev. A 80, 033838 (2009)
Katz, N., Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., O’Connell, A., Wang, H., Cleland, A.N., Martinis, J.M., Korotkov, A.N.: Reversal of the weak measurement of a quantum state in a super-conducting phase qubit. Phys. Rev. Lett. 101, 200401 (2008)
Kim, Y.-S., Cho, Y.-W., Ra, Y.-S., Kim, Y.-H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)
Korotkov, A.N., Keane, K.: Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81(R), 040103 (2010)
Lee, J.-C., Jeong, Y.-C., Kim, Y.-S., Kim, Y.-H.: Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 16309 (2011)
Sun, Q., Al-Amri, M., Davidovich, L., Zubairy, M.S.: Reversing entanglement change by a weak measure-ment. Phys. Rev. A 82, 052323 (2010)
Kim, Y.-S., Lee, J.-C., Kwon, O., Kim, Y.-H.: Protecting entanglement from decoherence using weak measure-ment and quantum measurement reversal. Nature Phys. 8, 117 (2012)
Carvalho, A.R.R., Reid, A.J.S., Hope, J.J.: Controlling entanglement by direct quantum feedback. Phys. Rev. A 78, 012334 (2008)
Yamamoto, N., Nurdin, H.I., James, M., Petersen, I.R.: Avoiding entanglement sudden death via measurement feedback control in a quantum network. Phys. Rev. A 78, 042339 (2008)
Chathavalappil, N., Satyanarayana, S.V.M.: Schemes to avoid entanglement sudden death of decohering two qubit system. Eur. Phys. J. D 3 (2019)
Lee, J.C., Lim, H.T., Hong, K.H., Jeong, Y.C., Kim, M.S., Kim, Y.H.: Experimental demonstration of delayed-choice decoherence suppression. Nat. Commun. 5, 4522 (2014)
Viola, L., Knill, E., Lloyd, S.: Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417 (1999)
Pan, Y., Xi, Z.R., Gong, J.: Optimized dynamic decoupling sequences in protecting two-qubit states. J. Phys. B: At. Mol. Opt. 44, 175501 (2011)
Lidar, D.A., Chuang, I.L., Whaley, K.B.: Decoherence-Free Subspaces for quantum computation. Phys. Rev. Lett. 81, 2594 (1998)
Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, K.G.: Science, experimental verification of decoherence-free subspaces. Science 290, 5491 (2000)
Facchi, P., Lidar, D.A., Pascazio, S.: Unification of dynamical decoupling and the quantum Zeno effect. Phys. Rev. A 69, 032314 (2004)
Maniscalco, S., Francica, F., Zaffino, R.L., Gullo, N.L., Plastina, F.: Protecting entanglement via the quantum zeno effect. Phys. Rev. Lett. 100, 090503 (2008)
Munro, W.J., James, D.F.V., White, A.G., Kwiat, P.G.: Maximizing the entanglement of two mixed qubits. Phys. Rev. A 64, 030302 (2001)
Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Acknowledgments
The first author Kapil K. Sharma acknowledges support from the Laboratory of Information Technology situated at Joint Institute For Nuclear Research, Dubna, Moscow Oblast. The contribution of second author Vladimir P. Gerdt was partially supported by the RUDN University Program (5–100).
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Appendix: Operators for Quantum Channels
Appendix: Operators for Quantum Channels
Kraus Operators → | E 1 | E 2 | E 3 | E 4 |
---|---|---|---|---|
Bit Flip | \( \left [\begin {array}{cc} \sqrt {p} & 0\\ 0 & \sqrt {p} \end {array}\right ] \) | \( \left [\begin {array}{cc} 0 & \sqrt {(1-p)}\\ \sqrt {(1-p)} & 0 \end {array}\right ] \) | ∙ | ∙ |
Phase flip | \(\left [\begin {array}{cc} \sqrt {p} & 0\\ 0 & \sqrt {p} \end {array}\right ]\) | \(\left [\begin {array}{cc} \sqrt {(1-p)} & 0 \\ 0 & \sqrt {(1-p)} \end {array}\right ]\) | ∙ | ∙ |
Bit Phase flip | \(\left [\begin {array}{cc}\sqrt {p} & 0\\ 0 & \sqrt {p} \end {array}\right ]\) | \(\left [\begin {array}{cc} 0 & -i\sqrt {(1-p)}\\ i\sqrt {(1-p)} & 0 \end {array}\right ]\) | ∙ | ∙ |
Amplitude damping | \( \left [\begin {array}{cc} 1 & 0\\ 0 & \sqrt {e^{-\gamma t}} \end {array}\right ]\) | \(\left [\begin {array}{cc} 0 & \sqrt {1-e^{-\gamma t}}\\ 0 & 0 \end {array}\right ]\) | ∙ | ∙ |
Phase damping | \(\left [\begin {array}{cc} \sqrt {e^{-\gamma t}} & 0\\ 0 & \sqrt {e^{-\gamma t}} \end {array}\right ]\) | \(\left [\begin {array}{cc} \sqrt {1-e^{-\gamma t}} & 0\\ 0 & 0 \end {array}\right ]\) | ⋆1 | ∙ |
Depolarization | \(\left [\begin {array}{cc} \sqrt {e^{-\gamma t}} & 0\\ 0 & \sqrt {e^{-\gamma t}} \end {array}\right ]\) | \(\left [\begin {array}{cc} 0 & \sqrt {\frac {1}{3}(1-e^{-\gamma t})} \\ \sqrt {\frac {1}{3}(1-e^{-\gamma t})} & 0 \end {array}\right ]\) | ⋆2 | ⋆3 |
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Sharma, K.K., Gerdt, V.P. Entanglement Sudden Death and Birth Effects in Two Qubits Maximally Entangled Mixed States Under Quantum Channels. Int J Theor Phys 59, 403–414 (2020). https://doi.org/10.1007/s10773-019-04332-z
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DOI: https://doi.org/10.1007/s10773-019-04332-z