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A NOTE ON MARKOVIAN QUANTUM DYNAMICS

Part of: General convexity General quantum mechanics and problems of quantization

Published online by Cambridge University Press:  15 May 2017

L. CHEN Open the ORCID record for L. CHEN [Opens in a new window] ,
H. X. MENG Open the ORCID record for H. X. MENG [Opens in a new window] ,
H. X. CAO Open the ORCID record for H. X. CAO [Opens in a new window] ,
Y. F. HUANG Open the ORCID record for Y. F. HUANG [Opens in a new window]  and
Y. YANG Open the ORCID record for Y. YANG [Opens in a new window]
L. CHEN
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi’an, China email b13128@snnu.edu.cn email menghuixian@snnu.edu.cn email caohx@snnu.edu.cn Department of Mathematics, Changji College, 831100 Changji, China email huangyongfeng@snnu.edu.cn
H. X. MENG
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi’an, China email b13128@snnu.edu.cn email menghuixian@snnu.edu.cn email caohx@snnu.edu.cn
H. X. CAO*
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi’an, China email b13128@snnu.edu.cn email menghuixian@snnu.edu.cn email caohx@snnu.edu.cn
Y. F. HUANG
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi’an, China email b13128@snnu.edu.cn email menghuixian@snnu.edu.cn email caohx@snnu.edu.cn Department of Mathematics, Changji College, 831100 Changji, China email huangyongfeng@snnu.edu.cn
Y. YANG
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi’an, China email b13128@snnu.edu.cn email menghuixian@snnu.edu.cn email caohx@snnu.edu.cn Department of Applied Mathematics, Yuncheng University, 044000 Yuncheng, China email yangyingyy@snnu.edu.cn
*
✉ caohx@snnu.edu.cn
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Abstract

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Based on the definition of divisibility of Markovian quantum dynamics, we discuss the Markovianity of tensor products, multiplications and some convex combinations of Markovian quantum dynamics. We prove that the tensor product of two Markovian dynamics is also a Markovian dynamics and propose a new witness of non-Markovianity.

Keywords

quantum Markovianitydivisibilitywitness

MSC classification

Primary: 81S22: Open systems, reduced dynamics, master equations, decoherence
Secondary: 81P40: Quantum coherence, entanglement, quantum correlations 52A37: Other problems of combinatorial convexity

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 436 - 445
Copyright
© 2017 Australian Mathematical Society 

References

Ali, Md. M., Lo, P. Y., Tu, M. W.-Y. and Zhang, W. M., “Non-Markovianity measure using two-time correlation functions”, Phys. Rev. A 92 (2015) 062306; doi:10.1103/PhysRevA.92.062306.CrossRefGoogle Scholar
Breuer, H. P., “Foundations and measures of quantum non-Markovianity”, J. Phys. B 45 (2012) 154001; doi:10.1088/0953-4075/45/15/154001.CrossRefGoogle Scholar
Breuer, H. P., Laine, E. M. and Piilo, J., “Measure for the degree of non-Markovian behavior of quantum processes in open systems”, Phys. Rev. Lett. 103 (2009) 210401; doi:10.1103/PhysRevLett.103.210401.CrossRefGoogle ScholarPubMed
Bylicka, B., Chruściński, D. and Maniscalco, S., “Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective”, Sci. Rep. 4 (2014) 5720; doi:10.1038/srep05720.CrossRefGoogle ScholarPubMed
Chin, A. W., Huelga, S. F. and Plenio, M. B., “Quantum metrology in non-Markovian environments”, Phys. Rev. Lett. 109 (2012) 233601; doi:10.1103/PhysRevLett.109.233601.CrossRefGoogle ScholarPubMed
Chruściński, D. and Kossakowski, A., “Witnessing non-Markovianity of quantum evolution”, Eur. Phys. J. D 68 (2014) 7; doi:10.1140/epjd/e2013-40171-9.CrossRefGoogle Scholar
Chruściński, D. and Maniscalco, S., “Degree of non-Markovianity of quantum evolution”, Phys. Rev. Lett. 112 (2014) 120404; doi:10.1103/PhysRevLett.112.120404.CrossRefGoogle ScholarPubMed
Chruściński, D. and Wudarski, F. A., “Non-Markovian random unitary qubit dynamics”, Phys. Lett. A 377 (2013) 1425–1429; doi:10.1016/j.physleta.2013.04.020.CrossRefGoogle Scholar
Chruściński, D. and Wudarski, F. A., “Non-Markovianity degree for random unitary evolution”, Phys. Rev. A 91 (2015) 012104; doi:10.1103/PhysRevA.91.012104.CrossRefGoogle Scholar
Hall, M. J. W., Cresser, J. D., Li, L. and Andersson, E., “Canonical form of master equations and characterization of non-Markovianity”, Phys. Rev. A 89 (2014) 042120; doi:10.1103/PhysRevA.89.042120.CrossRefGoogle Scholar
Hou, S. C., Liang, S. L. and Yi, X. X., “Non-Markovianity and memory effects in quantum open systems”, Phys. Rev. A 91 (2015) 012109; doi:10.1103/PhysRevA.91.012109.CrossRefGoogle Scholar
Lu, X. M., Wang, X. and Sun, C. P., “Quantum Fisher information flow and non-Markovian processes of open systems”, Phys. Rev. A 82 (2010) 042103; doi:10.1103/PhysRevA.82.042103.CrossRefGoogle Scholar
Luo, S., Fu, S. and Song, H., “Quantifying non-Markovianity via correlations”, Phys. Rev. A 86 (2012) 044101; doi:10.1103/PhysRevA.86.044101.CrossRefGoogle Scholar
Nielsen, M. A. and Chuang, I. L., Quantum computation and quantum information, 10th anniversary edn (Cambridge University Press, New York, 2010); doi:10.1017/CBO9780511976667.Google Scholar
Raginsky, M., “A fidelity measure for quantum channels”, Phys. Lett. A 290 (2001) 11–18; doi:10.1016/S0375-9601(01)00640-5.CrossRefGoogle Scholar
Rajagopal, A. K., Usha Devi, A. R. and Rendell, R. W., “Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian forms”, Phys. Rev. A 82 (2010) 042107; doi:10.1103/PhysRevA.82.042107.CrossRefGoogle Scholar
Rivas, Á. and Huelga, S. F., Open quantum systems: an introduction (Springer, Heidelberg, 2012); doi:10.1007/978-3-642-23354-8.CrossRefGoogle Scholar
Rivas, Á., Huelga, S. F. and Plenio, M. B., “Entanglement and non-Markovianity of quantum evolutions”, Phys. Rev. Lett. 105 (2010) 050403; doi:10.1103/PhysRevLett.105.050403.CrossRefGoogle ScholarPubMed
Rivas, Á., Huelga, S. F. and Plenio, M. B., “Quantum non-Markovianity: characterization, quantification and detection”, Rep. Progr. Phys. 77 (2014) 094001; doi:10.1088/0034-4885/77/9/094001.CrossRefGoogle ScholarPubMed
Shabani, A., Roden, J. and Whaley, K. B., “Continuous measurement of a non-Markovian open quantum system”, Phys. Rev. Lett. 112 (2014) 113601; doi:10.1103/PhysRevLett.112.113601.CrossRefGoogle ScholarPubMed
Vasile, R., Olivares, S., Paris, M. G. A. and Maniscalco, S., “Continuous-variable quantum key distribution in non-Markovian channels”, Phys. Rev. A 83 (2011) 042321; doi:10.1103/PhysRevA.83.042321.CrossRefGoogle Scholar
Wolf, M. M., Eisert, J., Cubitt, T. S. and Cirac, J. I., “Assessing non-Markovian quantum dynamics”, Phys. Rev. Lett. 101 (2008) 150402; doi:10.1103/PhysRevLett.101.150402.CrossRefGoogle ScholarPubMed