Full counting statistics of information content and particle number

Utsumi, Yasuhiro

doi:10.1103/physrevb.96.085304

Cited by 5 publications

(20 citation statements)

References 77 publications

(151 reference statements)

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“…However, it is not universal and depends on the setup; in order to obtain this form, we assume that the DOS is energy independent in Eq. (34). Moreover, Eq.…”

Section: A Averagesmentioning

confidence: 95%

“…In such a case, we can regard [ρ A ,Q A ] ≈ 0 and circumvent this problem. Another purpose of the present paper is to extend the multi-contour Keldysh Green function technique [31][32][33][34][35][36] . From this point of view, the present paper relies on our previous works [33][34][35] .…”

Section: Figmentioning

confidence: 99%

“…In Ref. 34, we accounted for the local particle number constraint to analyze the accessible entanglement. In the present paper, we will account for the local heat quantity constraint, Eqs.…”

Section: Figmentioning

confidence: 99%

“…where m = 1, · · · , M − 1. The block-skew circulant matrix is block-diagonalized by the following discrete Fourier transform 33,34 ,…”

Section: Appendix A: Projection Operatormentioning

confidence: 99%

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Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Utsumi

2019

Phys. Rev. B

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We consider a bipartite quantum conductor and analyze fluctuations of heat quantity in a subsystem as well as self-information associated with the reduced-density matrix of the subsystem. By exploiting the multi-contour Keldysh technique, we calculate the Rényi entropy, or the information generating function, subjected to the constraint of the local heat quantity of the subsystem, from which the probability distribution of conditional self-information is derived. We present an equality that relates the optimum capacity of information transmission and the Rényi entropy of order 0, which is the number of integer partitions into distinct parts. We apply our formalism to a twoterminal quantum dot. We point out that in the steady state, the reduced-density matrix and the operator of the local heat quantity of the subsystem may be commutative.

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“…However, it is not universal and depends on the setup; in order to obtain this form, we assume that the DOS is energy independent in Eq. (34). Moreover, Eq.…”

Section: A Averagesmentioning

confidence: 95%

Section: Figmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

“…where m = 1, · · · , M − 1. The block-skew circulant matrix is block-diagonalized by the following discrete Fourier transform 33,34 ,…”

Section: Appendix A: Projection Operatormentioning

confidence: 99%

See 2 more Smart Citations

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Utsumi

2019

Phys. Rev. B

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“…[16] and developed in Refs. [17,18,19,20]. In those previous works, the operator representation was adopted.…”

Section: Introductionmentioning

confidence: 99%

Full counting statistics of information content

Utsumi

2019

Eur. Phys. J. Spec. Top.

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We review connections between the cumulant generating function of full counting statistics of particle number and the Rényi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the Rényi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication channel. The ratio of the self-information content to the number of bosons fluctuates. For a small boson occupation number, the average and the fluctuation of the ratio are enhanced.

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How Quantum Evolution with Memory is Generated in a Time-Local Way

2021

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Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory effects, the first uses a time-nonlocal memory kernel K, whereas the second achieves the same using a time-local generator G. Here we show that the two are connected by a simple yet general fixed-point relation:. This allows one to extract nontrivial relations between the two completely different ways of computing the time-evolution and combine their strengths. We first discuss the stationary generator, which enables a Markov approximation that is both nonperturbative and completely positive for a large class of evolutions. We show that this generator is not equal to the low-frequency limit of the memory kernel, but additionally "samples" it at nonzero characteristic frequencies. This clarifies the subtle roles of frequency dependence and semigroup factorization in existing Markov approximation strategies. Second, we prove that the fixed-point equation sums up the time-domain gradient / Moyal expansion for the time-nonlocal quantum master equation, providing nonperturbative insight into the generation of memory effects. Finally, we show that the fixed-point relation enables a direct iterative numerical computation of both the stationary and the transient generator from a given memory kernel. For the transient generator this produces non-semigroup approximations which are constrained to be both initially and asymptotically accurate at each iteration step.

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Full counting statistics of information content and particle number

Cited by 5 publications

References 77 publications

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Full counting statistics of information content

How Quantum Evolution with Memory is Generated in a Time-Local Way

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