Dynamics beyond completely positive maps: Some properties and applications
Open accessAbstract
Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment, or if the applied transformation is correlated with the state of the system. We provide a physically motivated definition of accessible non-CP maps and derive two necessary conditions for a map to be accessible. We also show that entanglement between the system and the environment is not necessary to generate a non-CP dynamics. We describe two simple approximations that may be sufficient for some problems in process tomography, and then outline what these methods may be able to tell us in other situations where non-CP dynamics naturally arise.
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A map is Hermitian if and only if it can be written as the difference of two completely positive maps.
“It turns out that there is a tight connection between CP and Hermitian maps [9, 11]: a map is Hermitian iff it can be written as the difference of two CP maps.”
From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [9]
Completely positive (CP) maps are a subset of Hermitian maps.
“Vanishing discord states are a subset of SL states, and CP maps are a subset of Hermitian maps; we use the SL construction to prove our main result about CP maps.”
From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [9]
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- Authors
- Carteret, H. A., Terno, D. R., & Życzkowski, K.
- Affiliations
- University of Calgary (CA)
- Macquarie University (AU)
- Jagiellonian University (PL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2008-04-18
- Volume
- 77
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2140437613
- Cited by
- 118
- References
- 47
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 4 · 2023: 7 · 2022: 2 · 2021: 4 · 2020: 5 · 2019: 5 · 2018: 6 · 2017: 10 · 2016: 9 · 2015: 9 · 2014: 3 · 2013: 6 · 2012: 9
- FWCI
- 16.39
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Homo Politicus (Academy of Humanities and Economics in Lodz) (submittedVersion, cc-by-nc-nd)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Government of Canada
- Imperial College London
- Mitacs
- Institut Périmètre de physique théorique
- Natural Sciences and Engineering Research Council of Canada
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- open quantum systems, quantum dynamical maps, accessible maps, process tomography
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