Relaxation process of quantum system: Stochastic Liouville equation and initial correlation

Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

doi:10.1103/physreva.82.022111

Cited by 22 publications

(20 citation statements)

References 40 publications

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“…[7] and discuss the relation to the generalized Lindblad equation [17]. We consider a qubit interacting with a classical environment, where the influence of the environment on the qubit is described by means of a classical stochastic process.…”

Section: Stochastic Dephasing With Initial Correlationmentioning

confidence: 99%

“…On the other hand, when we take the trace of the stochastic density matrixŴ (t; k ) over the Hilbert space of the qubit, we derive the probability distribution of the stochastic variable, P (t; k ) = TrŴ (t; k ). When the stochastic variable is subject to the homogeneous Markov process, the time evolution of the stochastic density matrixŴ (t; ) is determined by the stochastic Liouville equation [6,7] …”

Section: Stochastic Dephasing With Initial Correlationmentioning

confidence: 99%

“…When the stochastic variable is subject to the Gauss-Markov process, k becomes a continuous variable and the linear map L is replaced with [5][6][7] …”

Section: Stochastic Dephasing With Initial Correlationmentioning

confidence: 99%

“…When the influence of the environment on the relevant quantum system is described by means of a classical stochastic process, the time evolution of the whole system consisting of the quantum system and the stochastic process can be described by means of the stochastic Liouville equation [4][5][6][7]. Using the stochastic Liouville equation, we can systematically treat the case that there is an initial correlation between a quantum system and a stochastic process.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is organized as follows: In Sec. II, we briefly review the time evolution of an open quantum system, which is derived by means of the stochastic Liouville equation [5][6][7]. We take an initial correlation between a relevant quantum system and a stochastic process into account.…”

Section: Introductionmentioning

confidence: 99%

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Trace distance in stochastic dephasing with initial correlation

2011

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The time evolution of the trace distance between quantum states of a qubit which is placed under the influence of stochastic dephasing is investigated within the framework of the stochastic Liouville equation. When stochastic dephasing is subject to the homogeneous Gauss-Markov process, the trace distance is exactly calculated in the presence of the initial correlation between the qubit and the stochastic process, where the stochastic process is inevitably a nonstationary process. It is found that even the initial correlation with the classical environment can make the trace distance greater than the initial value if stochastic dephasing causes the slow modulation of the qubit.

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Section: Stochastic Dephasing With Initial Correlationmentioning

confidence: 99%

Section: Stochastic Dephasing With Initial Correlationmentioning

confidence: 99%

“…When the stochastic variable is subject to the Gauss-Markov process, k becomes a continuous variable and the linear map L is replaced with [5][6][7] …”

Section: Stochastic Dephasing With Initial Correlationmentioning

confidence: 99%