Abstract
In this work, we mainly investigate effect of PT-symmetric operation on the dynamic behavior of the relative entropy of coherence for a two-level system within non-Markovian environments and put forward a feasible physical scheme to recover coherence by utilizing optimal PT-symmetric operation. The results show that the damaged quantum coherence can be effectively restored under influence of the non-Markovian regimes. Furthermore, the freezing phenomenon of the coherence can be detected by using the optimal PT-symmetric operation strength within the non-Markovian environments.
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References
Aberg, J.: Quantifying superposition. arXiv:quant-ph/0612146 (2006)
Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)
Winter, A., Yang, D.: Operational resource theory of coherence. Phys. Rev. Lett. 116, 120404 (2016)
Glauber, R.J.: Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963)
Sudarshan, E.C.G.: Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277 (1963)
Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)
Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)
Killoran, N., Steinhoff, F.E.S., Plenio, M.B.: Converting nonclassicality into entanglement. Phys. Rev. Lett. 116, 080402 (2016)
Chitambar, E., Streltsov, A., Rana, S., Bera, M.N., Adesso, G., Lewenstein, M.: Assisted distillation of quantum coherence. Phys. Rev. Lett. 116, 070402 (2016)
Chitambar, E., Gour, G.: Critical examination of incoherent operations and a physically consistent resource theory of quantum coherence. Phys. Rev. Lett. 117, 030401 (2016)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)
Bennett, C.H., Brassard, G., Crpeau, 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 (1993)
Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)
Bartlett, S.D., Rudolph, T., Spekkens, R.W.: Reference frames, superselection rules, and quantum information. Rev. Mod. Phys. 79, 555 (2007)
Gour, G., Spekkens, R.W.: Fundamental limitations for quantum and nanoscale thermodynamics. New J. Phys. 10, 033023 (2008)
Gour, G., Marvian, I., Spekkens, R.W.: Measuring the quality of a quantum reference frame: the relative entropy of frameness. Phys. Rev. A 80, 012307 (2009)
Brandäo, F.G.S.L., Horodecki, M., Oppenheim, J., Renes, J.M., Spekkens, R.W.: Resource theory of quantum states out of thermal equilibrium. Phys. Rev. Lett. 111, 250404 (2013)
Bowles, J., Vertesi, T., Quintino, M.T., Brunner, N.: One-way Einstein-Podolsky-Rosen steering. Phys. Rev. Lett. 112, 200402 (2014)
Costa, A.C.S., Angelo, R.M.: Quantification of Einstein-Podolski-Rosen steering for two-qubit states. Phys. Rev. A 93, 020103 (2016)
Wang, Y.T., Tang, J.S., Li, C.F.: Directly measuring the degree of quantum coherence using interference fringes. Phys. Rev. Lett. 118, 020403 (2017)
He, Z., Zeng, H.-S., Li, Y., Wang, Q., Yao, C.: Non-markovianity measure based on the relative entropy of coherence in an extended space. Phys. Rev. A 96, 022106 (2017)
Bellomo, B., Franco, R.L., Compagno, G.: Non-markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)
Garraway, B.M.: Nonperturbative decay of an atomic system in a cavity. Phys. Rev. A 55, 2290 (1997)
Maniscalco, S., Petruccione, F.: Non-markovian dynamics of a qubit. Phys. Rev. A 73, 012111 (2006)
Himadri, S.D., Manabendra, N.B., Gerardo, A.: Characterizing non-Markovianity via quantum interferometric power. Phys. Rev. A 91, 032115 (2015)
Chanda, T., Samyadeb, B.: Delineating incoherent non-Markovian dynamics using quantum coherence. Ann. Phys. 366, 1 (2016)
Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT-symmetry. Phys. Rev. Lett. 80, 5243 (1998)
Bender, C.M., Brody, D.C., Jones, H.F.: Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)
Bender, C.M.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947 (2006)
Sergi, A., Zloshchastiev, K.G.: Non-hermitian quantum dynamics of a two-level system and models of dissipative environments. Int. J. Mod. Phys. B 27, 1345053 (2013)
Sergi, A., Zloshchastiev, K.G.: Time correlation functions for non-Hermitian quantum systems. Phys. Rev. A 91, 062108 (2015)
Lee, Y.C., Hsieh, M.H., Flammia, S.T., Lee, R.K.: Local PT-symmetry violates the no-signaling principle. Phys. Rev. Lett. 112, 130404 (2014)
Bender, C.M., Brody, D.C., Jones, H.F., Meister, B.K.: Faster than Hermitian quantum mechanics. Phys. Rev. Lett. 98, 040403 (2007)
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This work is financially supported by the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 15A015).
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Leng, Y., Zhao, YH. Effect of PT-Symmetric Operator on Coherence Under the Non-Markovian Environments. Int J Theor Phys 58, 1874–1881 (2019). https://doi.org/10.1007/s10773-019-04082-y
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DOI: https://doi.org/10.1007/s10773-019-04082-y