An intuitive and natural way to quantify memory effects through measures on a probe quantum system is given from the aspect of sensitivity of environmental state. After several measures on the probe system, the degree of memory effects is given by the maximum distinguishability of output states of probe system corresponding to the variation of past evolution time. Quantum Fisher information on the past evolution duration which reflects the sensitivity of environmental state with respect to the system–environment evolution duration becomes the characteristic parameter of memory degree. The estimation process is applied on both classical and quantum environments, and the memory degree from the aspect of sensitivity of environmental state reflects the memory speed of environment.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Breuer, H., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)
Breuer, H.-P., Laine, E.-M., Piilo, J.: Measure for the degree of non-markovian behavior of quantum processes in open systems. Phys. Rev. Lett. 103, 210401 (2009)
Rivas, A., Huelga, S.F., Plenio, M.B.: Entanglement and non-markovianity of quantum evolutions. Phys. Rev. Lett. 105, 050403 (2010)
Hou, S.C., Yi, X.X., Yu, S.X., Oh, C.H.: Alternative non-markovianity measure by divisibility of dynamical maps. Phys. Rev. A 83, 062115 (2011)
Lu, X.-M., Wang, X., Sun, C.P.: Quantum fisher information flow and non-markovian processes of open systems. Phys. Rev. A 82, 042103 (2010)
Mazzola, L., Rodríguez-Rosario, C.A., Modi, K., Pater-nostro, M.: Dynamical role of system-environment correlations in non-Markovian dynamics. Phys. Rev. A 86, 010102 (2012)
Rodríguez-Rosario, C.A., Modi, K., Mazzola, L., Aspuru-Guzik, A.: Unification of witnessing initial system-environment correlations and witnessing non-Markovianity. Europhys. Lett. 99, 20010 (2012)
Rodríguez-Rosario, C.A., Modi, K., Kuah, A.-M., Shaji, A., Sudarshan, E.: Completely positive maps and classical correlations. J. Phys. A 41, 205301 (2008)
Modi, K.: Operational approach to open dynamics and quantifying initial correlations. Sci. Rep. 2, 581 (2012)
Laine, E.-M., Piilo, J., Breuer, H.-P.: Witness for initial system-environment correlations in open-system dynamics. Europhys. Lett. 92, 60010 (2010)
Gessner, M., Breuer, H.-P.: Detecting nonclassical system-environment correlations by local operations. Phys. Rev. Lett. 107, 180402 (2011)
Gessner, M., Ramm, M., Pruttivarasin, T., Buchleitner, A., Breuer, H.-P., Haffner, H.: Local detection of quantum correlations with a single trapped ion. Nat. Phys. 10, 105 (2014)
Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86, 044101 (2012)
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)
Fanchini, F.F., Karpat, G., Çakmak, B., Castelano, L.K., Aguilar, G.H., Farías, O.J., Walborn, S.P., Ribeiro, P.H.S., de Oliveira, M.C.: Non-markovianity through accessible information. Phys. Rev. Lett. 112, 210402 (2014)
Bylicka, B., Chruściński, D., Maniscalco, S.: Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective. Sci. Rep. 4, 5720 (2014)
Pineda, C., Gorin, T., Davalos, D., Wisniacki, D.A., García-Mata, I.: Measuring and using non-Markovianity. Phys. Rev. A 93, 022117 (2016)
Bylicka, B., Johansson, M., Acin, A.: Constructive method for detecting the information backflow of bijective non-completely-positive-divisible dynamics. arXiv: 1603.04288 (2016)
Usha Devi, A.R., Rajagopal, A.K., Sudha: Open-system quantum dynamics with correlated initial states, not completely positive maps, and non-Markovianity. Phys. Rev. A 83, 022109 (2011)
Wolf, M.M., Eisert, J., Cubitt, T.S., Cirac, J.I.: Assessing non-markovian quantum dynamics. Phys. Rev. Lett. 101, 150402 (2008)
Usha Devi, A.R., Rajagopal, A.K., Shenoy, S., Rendell, R.W.: Interplay of quantum stochastic and dynamical maps to discern markovian and non-markovian transitions. J. Quant. Inf. Sci. 2, 47 (2012)
Chruścińskiand, D., Maniscalco, S.: Degree of non-markovianity of quantum evolution. Phys. Rev. Lett. 112, 120404 (2014)
Pollock, F.A., Rodríguez-Rosario, C., Frauenheim, T., Paternostro, M., Modi, K.: Operational markov condition for quantum processes. Phys. Rev. Lett. 120, 040405 (2018)
Pollock, F.A., Rodríguez-Rosario, C., Frauenheim, T., Paternostro, M., Modi, K.: Non-Markovian quantum processes: complete framework and efficient characterization. Phys. Rev. A 97, 012127 (2018)
Budini, A.A.: Quantum non-markovian processes break conditional past-future independence. Phys. Rev. Lett. 121, 240401 (2018)
Budini, A.A.: Conditional past-future correlation induced by non-Markovian dephasing reservoirs. Phys. Rev. A 99, 052125 (2019)
Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)
Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam (1982)
Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)
Zurek, W.H.: Environment-induced superselection rules. Phys. Rev. D 26, 1862 (1982)
Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)
Cucchietti, F.M., Paz, J.P., Zurek, W.H.: Decoherence from spin environments. Phys. Rev. A 72, 052113 (2005)
Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87, 022337 (2013)
Anderson, P.W., Weiss, P.R.: Exchange narrowing in paramagnetic resonance. Rev. Mod. Phys. 25, 269 (1953)
Callaghan, P.T.: Principles of Nuclear Magnetic Resonance Microscopy. Clarendom Press, Oxford (1991)
This work was supported by the National Natural Science Foundation of China under Grants No. 11605030, the science and technology top talent support program of Guizhou educational department under Grant No. QJHKYZ084 and the academic new talent program of Guizhou department of Science and Technology under Grant No. GYU-KJT-23.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Jin, Y. Quantifying environmental memory degree from the aspect of environmental sensitivity. Quantum Inf Process 20, 77 (2021). https://doi.org/10.1007/s11128-021-03020-4
- Memory degree
- Environmental sensitivity
- Memory speed