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Cited by 10,118Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum many-body systems

Quantum entanglement

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Horodecki, Ryszard, Horodecki, Paweł, Horodecki, Michał, Horodecki, Karol·2009·Reviews of Modern Physics
DOI 10.1103/revmodphys.81.865
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Abstract

All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism---entanglement, recognized by Einstein, Podolsky, Rosen, and Schr\"odinger---waited over $70\phantom{\rule{0.3em}{0ex}}\text{years}$ to enter laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, has potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. However, it appears that this new resource is complex and difficult to detect. Although it is usually fragile to the environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation, and quantification. In particular, various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, and quantum cryptography are discussed, and some interrelations are pointed out. The basic role of entanglement in quantum communication within a distant laboratory paradigm is stressed, and some peculiarities such as the irreversibility of entanglement manipulations are also discussed including its extremal form---the bound entanglement phenomenon. The basic role of entanglement witnesses in detection of entanglement is emphasized.

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Crossref · 10.1103/revmodphys.81.865

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48 of 48 references verified0 citation errors · 0 not checkable

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  • The AMPS paradox states that for a sufficiently old black hole the outgoing Hawking modes must be nearly maximally entangled both with their ingoing partners and the early Hawking radiation, which would violate entanglement monogamy.

    “The latter is a statement that for a sufficiently old black hole the outgoing Hawking modes must be (nearly maximally) entangled both with their ingoing partners and the early Hawking radiation, which would violate the fundamental property of quantum mechanics -the entanglement monogamy [81].”

    From Conformal Cyclic Cosmology, gravitational entropy and quantum information (2023) · cites this paper as [81]

  • Unitary evaporation seems to conflict with basic theorems of quantum mechanics such as no-cloning and entanglement monogamy, which in turn threatens the relativistic causal structure.

    “Furthermore, the unitary evaporation seems to conflict with the basics theorems of quantum mechanics [67], such as no-cloning and entanglement monogamy [81], which in turn puts threat on the relativistic causal structure [82].”

    From Conformal Cyclic Cosmology, gravitational entropy and quantum information (2023) · cites this paper as [81]

  • Quantum entanglement cannot increase through LOCC (local operations and classical communication).

    “More directly, it is well-known that quantum entanglement cannot increase through LOCC (local operations and classical communication) [81].”

    From Conformal Cyclic Cosmology, gravitational entropy and quantum information (2023) · cites this paper as [81]

  • Any measure M defined as the distance from F_m using a contractive metric C is a resource quantifier and is non-increasing under any map in NR_m.

    “where C is a contractive metric, is a resource quantifier and in particular non-increasing under any map in NR m (see e.g. [4, 5]).”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [5]

  • Both the robustness and the relative entropy measure are monotones under NR, convex, and faithful (zero iff ρ∈F_m).

    “Both the robustness and the relative entropy measure are monotones under NR . They are also both convex and faithful (see e.g. [4, 5]) in the sense that they are zero iff ρ ∈ F m .”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [5]

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Authors
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K.
Affiliations
University of Gdańsk (PL)
ORCID
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
2009-06-17
Volume
81
Issue
2
Pages
865-942
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.81.865
OpenAlex
W3037737784
Semantic Scholar
b2b81503312bbd4f77acb21ea04019f30e060f78
Cited by
10,118
References
48
Citations by year
2026: 658 · 2025: 1008 · 2024: 906 · 2023: 743 · 2022: 742 · 2021: 766 · 2020: 634 · 2019: 648 · 2018: 575 · 2017: 519 · 2016: 520 · 2015: 518 · 2014: 441 · 2013: 408 · 2012: 365
FWCI
353.11
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Reviews of Modern Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
quantum entanglement, entanglement detection, entanglement distillation, entanglement quantification, Bell inequalities, entropy inequality, entanglement witnesses, quantum cryptography, quantum teleportation, dense coding, bound entanglement, nonclassical correlations

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