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Quantum Markov semigroups for continuous-time open quantum random walk

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Abstract

Open quantum random walks in Attal et al. (Phys Lett A 376:1545–1548, 2012) are quantum generalizations of classical Markov chains. In this paper, we firstly consider a problem to construct a quantum Markov semigroup (QMS) \({\mathcal {T}}_{t}\) directly from a continuous-time open quantum random walk (CTOQRW) developed in Pellegrini (J Stat Phys 154(3):838–865, 2014) and characterize its generator as well as its predual semigroup \({\mathcal {T}}_{*t}\). We show that this type of CTOQRWs brings about a large field of exploration for the behavior of open quantum system. Finally, we discuss some properties of this type of QMS constructed from CTOQRWs.

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  1. School of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Yuan Bao Kang

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  1. Yuan Bao Kang
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Correspondence to Yuan Bao Kang.

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This research is supported by the PhD program startup fund of Chongqing Normal University (Grant No. 15XL B013) and the National Natural Science fund advance research project of Chongqing Normal University (Grant No. 16XYY22).

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Kang, Y.B. Quantum Markov semigroups for continuous-time open quantum random walk. Quantum Inf Process 18, 196 (2019). https://doi.org/10.1007/s11128-019-2294-6

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  • DOI: https://doi.org/10.1007/s11128-019-2294-6

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