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The classical-quantum boundary for correlations: Discord and related measures
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One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
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“However, note that this equation does not hold for local maps on the ancilla 1 1 ⊗ E [231,232].”
From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [231]
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Metadata
- Authors
- Modi, K., Brodutch, A., Cable, H., Paterek, T., & Vedral, V.
- Affiliations
- Centre for Quantum Technologies (SG)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2012-11-26
- Volume
- 84
- Issue
- 4
- Pages
- 1655-1707
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2082014836
- Semantic Scholar
- 1de3d1784cca4dc5dd2b0afb7050b4dd4c03e9ab
- Cited by
- 1,600
- References
- 373
- Citations by year
- 2026: 69 · 2025: 78 · 2024: 95 · 2023: 73 · 2022: 101 · 2021: 99 · 2020: 96 · 2019: 126 · 2018: 109 · 2017: 158 · 2016: 151 · 2015: 156 · 2014: 146 · 2013: 130 · 2012: 13
- FWCI
- 139.83
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- National University of Singapore (submittedVersion)
- DR-NTU (Nanyang Technological University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- John Templeton Foundation
- University of Oxford
- National Research Foundation
- Centre for Quantum Technologies
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum discord, quantum correlations, quantum-to-classical transition, nonclassicality, entanglement, mixed states, quantum thermodynamics, open-system dynamics, many-body physics, quantum advantage
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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