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Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach

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Wufu Shi, Yusui Chen, Quanzhen Ding, Jin Wang, Ting Yu

Quantum Physics · Submitted 27 Dec 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations.

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arXiv ID2212.13362 (version 4)
Pith IDTC3Q45D4, Pith's permanent record of this paper and its review
CitationJin Wang, Quanzhen Ding, Ting Yu, Wufu Shi, Yusui Chen. "Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach." arXiv:2212.13362 (2022). https://pith.science/paper/TC3Q45D4
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,593 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations. Our method has an expanded range of applicability for accommodating a variety of non-Markovian environments. We show the positivity-preserving master equation for a three-level system coupled to a dissipative bosonic environment as a particular example to exemplify our general approach. We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot guarantee positivity. Our work provides a consistent master equation for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. background 1.00 0.09 0.06 asserted 1.00
s1 However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. background 0.63 0.07 0.03 asserted 0.97
s2 In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations. contribution 0.97 0.95 0.72 asserted 1.00
s3 Our method has an expanded range of applicability for accommodating a variety of non-Markovian environments. contribution 0.52 0.73 0.12 asserted 0.99
s4 We show the positivity-preserving master equation for a three-level system coupled to a dissipative bosonic environment as a particular example to exemplify our general approach. contribution 0.76 0.93 0.09 asserted 0.99
s5 We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot guarantee positivity. contribution 0.61 0.89 0.07 asserted 1.00
s6 Our work provides a consistent master equation for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems. interpretation 0.83 0.81 0.48 asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.91 · evidence from proof or derivation 0.73.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations. Our method has an expanded range of applicability for accommodating a variety of non-Markovian environments. We show the positivity-preserving master equation for a three-level system coupled to a dissipative bosonic environment as a particular example to exemplify our general approach. We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot guarantee positivity. Our work provides a consistent master equation for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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