Alternative non-Markovianity measure by divisibility of dynamical maps
Open accessAbstract
By identifying non-Markovianity with nondivisibility, we propose a measure of non-Markovianity for quantum processes. Three examples are presented, and the measure of non-Markovianity is calculated and discussed for these examples. Comparisons with other measures of non-Markovianity are made. The present non-Markovianity measure has the merit that no optimization procedure is required and it is finite for any quantum process, which greatly enhances the practical relevance of the proposed measure.
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The time derivative of the trace distance between two states is negative for Markovian processes and positive for non-Markovian processes.
“The time derivative, t ¼ @ t k 1 t À 2 t k tr =2, of the trace distance between states 1;2 t has been shown to be negative (decrease of distinguishability) for Markovian processes and positive (increase of distinguishability) for non-Markovian processes.”
From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [44]
The damped Jaynes-Cummings model is Markovian in the weak-coupling regime where the coupling strength is less than half the spectral width.
“The dynamics is Markovian in the weak-coupling regime, 0 < =2.”
From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [44]
The positive sign of the trace-distance derivative has been interpreted as information backflow from the environment to the system.
“The latter has been interpreted as an information backflow from the environment to the system [44][45][46][47].”
From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [44]
Non-Markovian dynamics has been characterized by an increase in the distinguishability of quantum states as quantified by trace distance.
“Non-Markovian dynamics has been characterized by an increase of the distinguishability of quantum states quantified by their trace distance [44].”
From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [44]
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References 22 · Cited by 115
- Authors
- Hou, S. C., Yi, X. X., Yu, S. X., & Oh, C. H.
- Affiliations
- Dalian University of Technology (CN)
- Centre for Quantum Technologies (SG)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2011-06-22
- Volume
- 83
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1975485875
- Cited by
- 115
- References
- 22
- Citations by year
- 2026: 5 · 2025: 3 · 2024: 8 · 2023: 5 · 2022: 8 · 2021: 12 · 2020: 9 · 2019: 5 · 2018: 6 · 2017: 4 · 2016: 10 · 2015: 12 · 2014: 10 · 2013: 9 · 2012: 8
- FWCI
- 4.86
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- National University of Singapore (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- non-Markovianity, divisibility, dynamical maps, quantum processes, non-Markovianity measures, open quantum systems, quantum dynamical maps
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