×

Study of quantum correlation swapping with relative entropy methods. (English) Zbl 1333.81108

Summary: To generate long-distance shared quantum correlations (QCs) for information processing in future quantum networks, recently we proposed the concept of QC repeater and its kernel technique named QC swapping. Besides, we extensively studied the QC swapping between two simple QC resources (i.e., a pair of Werner states) with four different methods to quantify QCs [C. Xie et al., Quantum Inf. Process. 14, No. 2, 653–679 (2015; Zbl 1311.81090)]. In this paper, we continue to treat the same issue by employing other three different methods associated with relative entropies, i.e., the MPSVW method [K. Modi et al., “Unified view of quantum and classical correlations”, Phys. Rev. Lett. 104, No. 8, Article ID 080501, 4 p. (2010; doi:10.1103/PhysRevLett.104.080501)], the Zhang method [Z.-j. Zhang, “Revised definitions of quantum dissonance and quantum discord”, Preprint, arXiv:1011.4333] and the RS method [C. C. Rulli and M. S. Sarandy, “Global quantum discord in multipartite systems”, Phys. Rev. A 84, No. 4, Article ID 042109, 6 p. (2011; doi:10.1103/PhysRevA.84.042109)]. We first derive analytic expressions of all QCs which occur during the swapping process and then reveal their properties about monotonicity and threshold. Importantly, we find that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed. In addition, we simply compare our present results with our previous ones.

MSC:

81P68 Quantum computation
81P40 Quantum coherence, entanglement, quantum correlations

Citations:

Zbl 1311.81090
Full Text: DOI

References:

[1] Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001) · Zbl 1255.81071 · doi:10.1103/PhysRevLett.88.017901
[2] Luo, S.L.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008) · doi:10.1103/PhysRevA.77.042303
[3] Luo, S.L.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008) · doi:10.1103/PhysRevA.77.022301
[4] Luo, S.L., Fu, S.S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010) · Zbl 1255.81092 · doi:10.1103/PhysRevA.82.034302
[5] Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010) · doi:10.1103/PhysRevLett.104.080501
[6] Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010) · Zbl 1255.81213 · doi:10.1103/PhysRevLett.105.190502
[7] Girolami, D., Paternostro, M., Adesso, G.: Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states. J. Phys. A Math. Theor. 44, 352002 (2011) · Zbl 1227.81075 · doi:10.1088/1751-8113/44/35/352002
[8] Zhou, T., Cui, J., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011) · doi:10.1103/PhysRevA.84.062105
[9] Zhang, Z.J.: Revised definitions of quantum dissonance and quantum discord. arXiv:1011.4333 [quant-ph]
[10] Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011) · doi:10.1103/PhysRevA.84.042109
[11] Zhang, F.L., Chen, J.L.: Irreducible multiqutrit correlations in Greenberger-Horne-Zeilinger type states. Phys. Rev. A. 84, 062328 (2011) · doi:10.1103/PhysRevA.84.062328
[12] Wei, H.R., Ren, B.C., Deng, F.G.: Geometric measure of quantum discord for a two-parameter class of states in a qubit-qutrit system under various dissipative channels. Quantum Inf. Process. 12, 1109 (2013) · Zbl 1264.81101 · doi:10.1007/s11128-012-0458-8
[13] Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010) · doi:10.1103/PhysRevA.81.042105
[14] Hu, X.Y., et al.: Necessary and sufficient conditions for local creation of quantum correlation. Phys. Rev. A 85, 032102 (2012) · doi:10.1103/PhysRevA.85.032102
[15] Shi, M., Sun, C., Jiang, F., Yan, X., Du, J.: Optimal measurement for quantum discord of two-qubit states. Phys. Rev. A 85, 064104 (2012) · doi:10.1103/PhysRevA.85.064104
[16] Huang, Y.C.: Quantum discord for two-qubit X states: analytical formula with very small worst-case error. Phys. Rev. A 88, 014302 (2013) · doi:10.1103/PhysRevA.88.014302
[17] Huang, Y.C.: Scaling of quantum discord in spin models. Phys. Rev. B 89, 054410 (2014) · doi:10.1103/PhysRevB.89.054410
[18] Huang, Y.C.: Computing quantum discord is NP-complete. New J. Phys. 16, 033027 (2014) · Zbl 1451.81107 · doi:10.1088/1367-2630/16/3/033027
[19] Giorda, P., Paris, M.G.A.: Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010) · doi:10.1103/PhysRevLett.105.020503
[20] Hu, X., Fan, H., Zhou, D.L., Liu, W.M.: Quantum correlating power of local quantum channels. Phys. Rev. A 87, 032340 (2013) · doi:10.1103/PhysRevA.87.032340
[21] Hu, M.L., Fan, H.: Upper bound and shareability of quantum discord based on entropic uncertainty relations. Phys. Rev. A 88, 014105 (2013) · doi:10.1103/PhysRevA.88.014105
[22] Ye, B.L., Liu, Y.M., Chen, J.L., Liu, X.S., Zhang, Z.J.: Analytic expressions of quantum correlations in qutrit Werner states. Quantum Inf. Process. 12, 2355 (2013) · Zbl 1270.81038 · doi:10.1007/s11128-013-0531-y
[23] Tang, H.J., Liu, Y.M., Chen, J.L., Ye, B.L., Zhang, Z.J.: Analytic expressions of discord and geometric discord in Werner derivatives. Quantum Inf. Process. 13, 1331 (2014) · Zbl 1303.81028 · doi:10.1007/s11128-014-0731-0
[24] Li, G.F., Liu, Y.M., Tang, H.J., Yin, X.F., Zhang, Z.J.: Analytic expression of quantum correlations in qutrit Werner states undergoing local and nonlocal unitary operations. Quantum Inf. Process. 14, 559 (2015) · Zbl 1311.81032 · doi:10.1007/s11128-014-0888-6
[25] Xie, C.M., Liu, Y.M., Li, G.F., Zhang, Z.J.: A note on quantum correlations in Werner states under two collective noises. Quantum Inf. Process. 13, 2713 (2014) · Zbl 1304.81045 · doi:10.1007/s11128-014-0822-y
[26] Xie, C.M., Liu, Y.M., Xing, H., Chen, J.L., Zhang, Z.J.: Quantum correlation swapping. Quantum Inf. Process. 14, 653-679 (2015) · Zbl 1311.81090 · doi:10.1007/s11128-014-0875-y
[27] Madsen, L.S., Berni, A., Lassen, M., Andersen, U.L.: Experimental investigation of the evolution of Gaussian quantum discord in an open system. Phys. Rev. Lett. 109, 030402 (2012) · doi:10.1103/PhysRevLett.109.030402
[28] Lanyon, B.P., Jurcevic, P., Hempel, C., et al.: Experimental generation of quantum discord via noisy processes. Phys. Rev. Lett. 111, 100504 (2013) · doi:10.1103/PhysRevLett.111.100504
[29] Vogl, U., Glasser, R.T., Glorieux, Q., et al.: Experimental characterization of Gaussian quantum discord generated by four-wave mixing. Phys. Rev. A 87, 010101(R) (2013) · doi:10.1103/PhysRevA.87.010101
[30] Benedetti, C., Shurupov, A.P., Paris, M.G.A., et al.: Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations. Phys. Rev. A 87, 052136 (2013) · doi:10.1103/PhysRevA.87.052136
[31] Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011) · doi:10.1103/PhysRevA.83.032323
[32] Dakic, B., Lipp, Y.O., Ma, X., et al.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012) · doi:10.1038/nphys2377
[33] Li, B., Fei, S.M., Wang, Z.X., Fan, H.: Assisted state discrimination without entanglement. Phys. Rev. A 85, 022328 (2012) · doi:10.1103/PhysRevA.85.022328
[34] Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008) · doi:10.1103/PhysRevLett.100.050502
[35] Maziero, J., Céleri, L.C., Serra, R.M., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009) · doi:10.1103/PhysRevA.80.044102
[36] Streltsov, A., Kampermann, H., Bruss, D.: Behavior of quantum correlations under local noise. Phys. Rev. Lett. 107, 170502 (2011) · doi:10.1103/PhysRevLett.107.170502
[37] Ciccarello, F., Giovannetti, V.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85, 010102(R) (2012) · doi:10.1103/PhysRevA.85.010102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.