The quantum Markovianity criterion based on correlations under random unitary qudit dynamical evolutions

Xu, Wen Yong; Zheng, Zhu-Jun; Fei, Shao-Ming

doi:10.1007/s11128-022-03574-x

Quantum Inf Process

2022

DOI: 10.1007/s11128-022-03574-x

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The quantum Markovianity criterion based on correlations under random unitary qudit dynamical evolutions

Wen Yong Xu

Zhu-Jun Zheng

Shao-Ming Fei

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Cited by 4 publications

(2 citation statements)

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“…We then study how much the dynamics of the system is non-Markovian using already tested non-Markovianity measures [94][95][96][97][98][99][100][101][102][103][104][105]. This analysis is quite complex to perform as we need to use exact diagonalization techniques and simulate the dynamics many times, and thus the maximum system sizes that we can consider are limited.…”

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confidence: 99%

Measurement induced transitions in non-Markovian free fermion ladders

Tsitsishvili,

Poletti,

Dalmonte

et al. 2024

SciPost Phys. Core

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Recently there has been an intense effort to understand measurement induced transitions, but we still lack a good understanding of non-Markovian effects on these phenomena. To that end, we consider two coupled chains of free fermions, one acting as the system of interest, and one as a bath. The bath chain is subject to Markovian measurements, resulting in an effective non-Markovian dissipative dynamics acting on the system chain which is still amenable to numerical studies in terms of quantum trajectories. Within this setting, we study the entanglement within the system chain, and use it to characterize the phase diagram depending on the ladder hopping parameters and on the measurement probability. For the case of pure state evolution, the system is in an area law phase when the internal hopping of the bath chain is small, while a non-area law phase appears when the dynamics of the bath is fast. The non-area law exhibits a logarithmic scaling of the entropy compatible with a conformal phase, but also displays linear corrections for the finite system sizes we can study. For the case of mixed state evolution, we instead observe regions with both area, and non-area scaling of the entanglement negativity. We quantify the non-Markovianity of the system chain dynamics and find that for the regimes of parameters we study, a stronger non-Markovianity is associated to a larger entanglement within the system.

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confidence: 99%

Measurement induced transitions in non-Markovian free fermion ladders

Tsitsishvili,

Poletti,

Dalmonte

et al. 2024

SciPost Phys. Core

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“…e Tr H T H T tot tot [25,26], where H is the total Hamiltonian and Tr tot denotes the partial trace over the probe-environment state. Then the two-qubit probes state considering the initial correlations, which is governed by a Markovian process [16,26,27], can be written as…”

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confidence: 99%

Improving the accuracies of estimating environment parameters via initial probe-environment correlations

Zhang,

Gong

2024

Phys. Scr.

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We investigate the effect of the initial probe-environment correlations in estimating the environment parameters including cutoff frequency, coupling strength, and temperature, which are the crucial parameters characterizing the environment of an open quantum system. The two-qubit probe, referred to as a probe constructed by two qubits, is coupled with separate bosonic reservoirs and prepared in the product state. With the initial probe-environment correlations, we derive the analytic quantum Fisher information (QFI) and the corresponding quantum signal-to-noise ratio (QSNR) of any environment parameter, which quantify the estimation accuracy in the two-qubit probe scheme. By numerically comparing the QFI and QSNR with the initial probe-environment correlations to those without correlations, it shows the feasibility of the initial probe-environment correlations in improving the precision for environment parameter estimation.

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Markovian semigroup from mixing generalized Weyl dephasing channels

Xu,

Li,

Zheng

2024

Phys. Rev. A

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The quantum Markovianity criterion based on correlations under random unitary qudit dynamical evolutions

Cited by 4 publications

References 40 publications

Measurement induced transitions in non-Markovian free fermion ladders

Measurement induced transitions in non-Markovian free fermion ladders

Improving the accuracies of estimating environment parameters via initial probe-environment correlations

Markovian semigroup from mixing generalized Weyl dephasing channels

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