Abstract
In this paper, we aim to investigate the freezing of quantum coherence for Bell-diagonal states by using stochastic strictly incoherence operations in non-dissipative decoherence environments. We find that quantum coherence of the Bell-diagonal states, which is subject to the stochastic strictly incoherence operations, becomes more stable. The stochastic strictly incoherent operation not only increases quantum coherence, but also keeps the quantum coherence intact in decoherence channel. It means that quantum coherence can be frozen with the growth of the noisy strength. This is because the stochastic strictly incoherence operations are free ones, this process will not produce quantum coherence.
Similar content being viewed by others
References
Yuan, X., Zhou, H., Cao, Z., Ma, X.: Intrinsic randomness as a measure of quantum coherence. Phys. Rev. A. 92, 022124 (2015)
Aberg, J.: Catalytic coherence. Phys. Rev. Lett. 113, 150402 (2014)
Lostaglio, M., Jennings, D., Rudolph, T.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 6, 6383 (2015)
Lostaglio, M., Korzekwa, K., Jennings, D., Rudolph, T.: Quantum coherence, time-translation symmetry and thermodynamics. Phys. Rev. X. 5, 021001 (2015)
Engel, G. S.: Evidence for wavelike energy transfer through quantum coherence in photosynthetic system. Nature 446, 782 (2007). (London)
Ming, F., Wang, D., Shi, W.N., Huang, A.J., Sun, W.Y., Ye, L.: Entropic uncertainty relations in the Heisenberg XXZ model and its controlling via filtering operations. Quantum Inf. Process. 17, 89 (2018)
Ming, F., Wang, D., Shi, W.N., Huang, A.J., Du, M.M., Sun, W.Y., Ye, L.:Exploring uncertainty relation and its connection with coherence under the Heisenberg spin model with the Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 17, 267 (2018)
Du, M.M., Wang, D., Ye, L.: The dynamic behaviors of complementary correlations under decoherence channels. Sci. Rep. 7, 40934 (2017)
Breuer, H.P., Petruccione, F.: The Theory of Open Quantum System. Oxford University Press, Oxford (2002)
Girolami, D.: Observable measure of quantum coherence in finite dimensional system. Phys. Rev. Lett. 113, 170401 (2014)
Shao, L.H., Xi, Z., Fan, H., Li, Y.: Fidelity and trace-norm distances for quantifying coherence. Phys. Rev. A. 91, 042120 (2015)
Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)
Liu, X., Tian, Z.H., Wang, J.C., Jing, J.L.: Protecting quantum coherence of two-level atoms from vacuum fluctuations of electromagnetic field. Ann. Phys. 366, 102–112 (2016)
Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)
Yu, X.D., Zhang, D.J., Liu, C.L., Tong, D.M.: Measure-independent freezing of quantum coherence. Phys. Rev. A. 93, 060303(R) (2017)
Silva, I.A., Souza, A.M., Bromley, T.R., Cianciaruso, M., Marx, R., Sarthour, R.S., Oliveira, I.S., Lo Franco, R., Glaser, S.J., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Observation of time-invariant coherence in a nuclear magnetic resonance quantum simulator. Phys. Rev. Lett. 117, 160402 (2016)
Bromley, T.R., Cianciaruso, M., Franco, R.L., Adesso, G.: Unifying approach to the quantification of bipartite correlations by bures distance. Phys. A Math. Theor. 47, 405302 (2014)
Aaronson, B., Lo Franco, R., Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A. 88, 012120 (2013)
Aaronson, B., Lo Franco, R., Compagno, G., Adesso, G.: Hierarchy and dynamics of trace distance correlations. New J. Phys. 15, 093022 (2013)
Cianciaruso, M., Bromley, T.R., Roga, W., Lo Franco, R., Adesso, G.: Universal freezing of quantum correlations within the geometric approach. Sci. Rep. 5, 10177 (2015)
Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C., Andersson, E., Lo Franco, R., Compagno, G.: Experimental recovery of quantum correlations in absence of system environment back-action. Nat. Commun. 4, 2851 (2013)
Streltsov, A., Adesso, G., Plenio, M. B.: Quantum Coherence as a Resource. Rev. Mod. Phys. 89, 041003 (2017)
Liu, C.L., Guo, Y.Q., Tong, D.M.: Enhancing coherence of a state by stochastic strictly incoherence operations. Phys. Rev. A. 96, 062325 (2017)
Yadin, B., Ma, D., Girolami, M., Vedral, V.: Quantum processes which do not use coherence. Phys. Rev. X. 6, 041028 (2016)
Linden, N., Massar, S., Popescu, S.: Purifying noisy entanglement requires collection measurements. Phys. Rev. Lett. 81, 3279–3282 (1998)
Kent, A., et al.: Entanglement mixed states and local purification. Phys. Rev. Lett. 81, 2839 (1998)
Kent, A., Linden, N., Massar, S.: Optimal entanglement enhancement for mixed states. Phys. Rev. Lett. 83, 2656–2659 (1999)
Horodecki, R., Horodecki, M.: Information-theoretic aspects of inseparability of mixed states. Phys. Rev. A. 54, 1838–1843 (1996)
Baumgratz, T., Cramer, M., Plenio, M.D.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)
Bu, A., Sing, U., Wu, J.: Catalytic coherence transformations. Phys. Rev. A. 93, 042326 (2016)
Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement: a key issues review. Rep. Prog. Phys. 78, 042001 (2015)
Chang, J., Kwon, Y.: Entanglement behavior of quantum states of fermionic systems in an accelerated frame. Phys. Rev. A. 85, 032302 (2012)
Shi, J.D., Xu, S., Ma, W.C., Song, X.K., Ye, L.: Purifying two-qubit entanglement in nonidentical decoherence by employing weak measurements. Quantum Inf. Process. 14, 1387–1397 (2015)
Sun, W.Y., Wang, D., Shi, J.-D., Ye, L.: Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs. Sci. Rep. 7, 39651 (2017)
Sun, W.-Y., Wang, D., Yang, J., Ye, L.: Enhancement of multipartite entanglement in an open system under non-inertial frames. Quantum Inf. Process. 16, 90 (2017)
Acknowledgments
This work was supported by the National Science Foundation of China under Grant Nos. 11575001 and 61601002, Natural Science Foundation of Education Department of Anhui Province (Grant No. KJ2016SD49), and also the fund from CAS Key Laboratory of Quantum Information (Grant No. KQI201701).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, YS., Wang, D. & Ye, L. How Stochastic Strictly Incoherent Operations Affect Coherence in Decoherence Channels. Int J Theor Phys 58, 3667–3676 (2019). https://doi.org/10.1007/s10773-019-04235-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-019-04235-z