Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation
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We present a general analysis of the role of initial correlations between the open system and an environment on quantum dynamics of the open system.
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For an analytic time-dependence, the inverse of Φ(t,0) and the generator K(t) do exist apart from isolated singularities of the time axis.
“However, for an analytic time-dependence the inverse of Φ( t, 0) and the generator K ( t ) do exist apart from isolated singularities of the time axis [22].”
From Foundations and measures of quantum non-Markovianity (2012) · cites this paper as [22]
The problem of identifying the general physical conditions under which completely positive maps are valid had remained open since it was first posed.
“For this reason it is perhaps surprising that the problem of identifying the general physical conditions under which CP maps are valid has remained open since it was first posed in a vigorous debate [5, 6].”
From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [6]
If one gives up the consistency condition that the reduced system state equals the partial trace of the system-bath state for all system states, or gives up linearity except in the weak coupling regime, completely positive maps arise for more general initial states.
“If one gives up the consistency condition ρ S = Tr B [ ρ SB ] for all ρ S , or gives up linearity except in the weak coupling regime, CP maps arise for more general initial states [6].”
From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [6]
It was not known which is the most general class of states for which the quantum dynamical process is always completely positive for arbitrary joint unitaries.
“In particular, while sufficient conditions have been developed for complete positivity [6, 12], it is not known which is the most general class of states for which the QDP (1) is always CP, for arbitrary U SB .”
From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [6]
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Cites
Quantum theory of open systems
Davies, E. B. (1976) · Cited by 2,383 · see citing works
Reduced Dynamics Need Not Be Completely Positive
Pechukas, P. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.1060 · Cited by 462 · see citing works
Decoherence and initial correlations in quantum Brownian motion
Romero, L. C. D., & Paz, J. P. (1997) · Physical Review A · doi:10.1103/physreva.55.4070 · Cited by 100 · see citing works
Reconstruction of Liouvillian superoperators
Bužek, V. (1998) · Physical Review A · doi:10.1103/physreva.58.1723 · Cited by 39 · see citing works
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Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps
Shabani, A., & Lidar, D. A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.100402 · Cited by 309 · see citing works
Foundations and measures of quantum non-Markovianity
Breuer, H.-P. (2012) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/45/15/154001 · Cited by 225 · see citing works
Non-Markovian generalization of the Lindblad theory of open quantum systems
Breuer, H.-P. (2007) · Physical Review A · doi:10.1103/physreva.75.022103 · Cited by 196 · see citing works
Quantum process tomography of the quantum Fourier transform
Weinstein, Y. S., Havel, T. F., Emerson, J., Boulant, N., Saraceno, M., Lloyd, S., & Cory, D. G. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1785151 · Cited by 178 · see citing works
Initial correlations in open-systems dynamics: The Jaynes-Cummings model
Smirne, A., Breuer, H.-P., Piilo, J., & Vacchini, B. (2010) · Physical Review A · doi:10.1103/physreva.82.062114 · Cited by 125 · see citing works
Dynamics beyond completely positive maps: Some properties and applications
Carteret, H. A., Terno, D. R., & Życzkowski, K. (2008) · Physical Review A · doi:10.1103/physreva.77.042113 · Cited by 118 · see citing works
Experimental investigation of initial system-environment correlations via trace-distance evolution
Smirne, A., Brivio, D., Cialdi, S., Vacchini, B., & Paris, M. G. A. (2011) · Physical Review A · doi:10.1103/physreva.84.032112 · Cited by 96 · see citing works
Experimentally witnessing the initial correlation between an open quantum system and its environment
Li, C.-F., Tang, J.-S., Li, Y.-L., & Guo, G.-C. (2011) · Physical Review A · doi:10.1103/physreva.83.064102 · Cited by 66 · see citing works
Kraus representation in the presence of initial correlations
Hayashi, H., Kimura, G., & Ota, Y. (2003) · Physical Review A · doi:10.1103/physreva.67.062109 · Cited by 53 · see citing works
- Authors
- Štelmachovič, P., & Bužek, V.
- Affiliations
- Slovak Academy of Sciences (SK)
- ORCID
- Bužek, Vladimír
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-11-16
- Volume
- 64
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2021918581
- Cited by
- 173
- References
- 4
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 7 · 2023: 3 · 2022: 7 · 2021: 6 · 2020: 6 · 2019: 5 · 2018: 7 · 2017: 6 · 2016: 12 · 2015: 6 · 2014: 7 · 2013: 9 · 2012: 14
- FWCI
- 2.58
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (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
- open quantum systems, initial correlations, system-environment entanglement, quantum dynamics, Kraus representation, non-Markovian dynamics, quantum measurement
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