Abstract
Quantum discord is studied for two-qubit systems with different settings under the influence of the Bloch channel which is characterized by the longitudinal and transversal relaxation times and the environmental temperature. The relaxation of the quantum discord strongly depends on the ratio of the two relaxation times and the environmental temperature. It is found that the ratio of the quantum discord to the total correlation becomes finite or zero asymptotically, depending on the ratio of the relaxation times and the system setting. Furthermore, the optimal setting for sharing the quantum discord is discussed for given environmental temperature and ratio of the relaxation times.






Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)
Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)
Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)
Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A 34, 6899–6905 (2001)
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2002)
Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)
Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. 101, 20051 (2008)
Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011)
Ali, M., Rau, A.R., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)
Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 052107 (2010)
Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. Rev. 84, 042313 (2011)
Maldonade-Trapp, A., Hu, A., Roa, L.: Analytical solutions and criteria for the quantum discord of two-qubit X-states. Quantum Inf. Process. 14, 1947–1958 (2015)
Yurischev, M.A.: On quantum discord of general X states. Quantum Inf. Process. 14, 3399–3421 (2015)
Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)
Huang, Y.: Quantum discord for two-qubit X states: analytical formula with very small worst-case error. Phys. Rev. 88, 014302 (2013)
Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. 83, 052108 (2011)
Lu, X., Ma, J., Xi, Z., Wang, X.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. 83, 012327 (2011)
Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2006)
Alicki, R., Lendi, K.: Quantum Dynamical Semigroups and Applications. Springer, Berlin (2007)
Rivas, A., Huelga, S.F.: Open Quantum Systems. Springer, Berlin (2012)
Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)
Yu, T., Hberly, J.H.: Quantum open system theory: bipartite aspects. Phys. Rev. Lett. 97, 140403 (2006)
Almeida, M.P., de Melo, F., Hor-Meyll, M., Salles, A., Walborn, S.P., Rebeiro, P.H.S., Davidovich, L.: Environment-induced sudden death of entanglement. Science 316, 579–582 (2007)
Laurat, J., Choi, K.S., Deng, H., Chou, C.W., Kimble, H.J.: Heralded entanglement between atomic ensembles: preparation, decoherence, and scaling. Phys. Rev. Lett. 99, 180504 (2007)
Mundarain, D., Orszag, M.: Decoherence-free subspace and entanglement by interaction with a common squeezed bath. Phys. Rev. A 75, 040303 (2007)
Ikram, M., Li, F., Zubairy, M.S.: Disentanglement in a two-qubit system subjected to dissipation environments. Phys. Rev. A 75, 062336 (2007)
Hernandez, M., Orszag, M.: Decoherence and disentanglement for two qubits in a common squeezed reservoir. Phys. Rev. A 78, 042114 (2008)
Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009)
Maziero, J., Celeri, L.C., Serra, R.M., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009)
Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)
Chanda, T., Pal, A.K., Biswas, A., Sen, A., Sen, U.: Freezing of quantum correlations under local decoherence. Phys. Rev. A 91, 062119 (2015)
Maziero, J., Werlang, T., Fanchini, F.F., Celeri, L.C., Serra, R.M.: System-reservoir dynamics of quantum and classical correlations. Phys. Rev. A 81, 022116 (2010)
Hua, M., Tian, D.: Preservation of the geometric quantum discord in noisy environments. Ann. Phys. 343, 132–140 (2014)
Haikka, P., Johnson, T.H., Maniscalco, S.: Non-Markovianity of local dephasing channels and time-invariant discord. Phys. Rev. A 87, 010103 (2013)
Ma, W., Xu, S., Shi, J., Ye, L.: Quantum correlation versus Bell-inequality violation under the amplitude damping channel. Phys. Lett. A 379, 2802–2807 (2015)
Ciccarello, F., Giovannetti, V.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85, 010102 (2012)
Shi, J.D., Wang, D., Ma, W.C., Ye, L.: Enhancing quantum correlation in open-system dynamics by reliable quantum operations. Quantum Inf. Process. 14, 3569–3579 (2015)
Karmakar, S., Sen, A., Bhar, A., Sarkar, D.: Effect of local filtering on freezing phenomena of quantum correlation. Quantum Inf. Process. 14, 2517–2533 (2015)
Obada, A.S.F., Hessian, H.A., Mohamed, A.B.A., Hashem, M.: Stationary discord and non-local correlations via qubit damping. J. Mod. Opt. 62, 918–926 (2015)
Li, Y., Xiao, X.: Recovering quantum correlations from amplitude damping decoherence by weak measurement reversal. Quantum Inf. Process. 12, 3067–3077 (2013)
Wang, C., Li, C., Nie, L., Li, X., Li, J.: Classical correlation, quantum discord and entanglement for two-qubit system subject to heat bath. Opt. Commun. 284, 2393–2401 (2011)
Dajka, J., Mierzejewski, M., Luczka, J., Blattmann, R., Hänggi, L.: Negativity and quantum discord in Davies environment. J. Phys. A 45, 485306 (2012)
Ban, M., Kitajima, S., Shibata, F.: Decoherence of entanglement in Bloch channel. J. Phys. A 38, 4235–4245 (2005)
Ban, M.: Disentanglement of two-qubit system in the Bloch channel. Opt. Commun. 283, 3812–3817 (2010)
Ban, M.: Decay of two-qubit correlations in the squeezed Bloch channel. J. Mod. Opt. 59, 823–829 (2012)
Huang, Y.: Computing quantum discord as NP-complete. New J. Phys. 16, 033027 (2014)
Yu, T., Eberly, J.H.: Evolution from entanglement to decoherence of bipartite X states. Quantum Inf. Comp. 7, 459–468 (2007)
Dajka, J., Luczka, J.: Swapping of correlation via teleportation with decoherence. Phys. Rev. A 87, 022301 (2013)
Kloda, D., Dajka, J.: Temperature-independent teleportation of qubits in Davies environments. Quantum Inf. Process. 14, 135–145 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kondo, I., Ban, M. Quantum discord for two-qubit systems in the Bloch channel: effects of longitudinal and transversal relaxation times. Quantum Inf Process 16, 196 (2017). https://doi.org/10.1007/s11128-017-1651-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-017-1651-6