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Cited by 5,272Quantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

The DOI matches its Crossref record; 45 of the 45 references it cites were found in a registry or an index.

Mixed-state entanglement and quantum error correction

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Bennett, Charles H., DiVincenzo, David P., Smolin, John A., Wootters, William K.·1996·Physical Review A
DOI 10.1103/physreva.54.3824
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Abstract

Entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbitrary quantum state |\ensuremath{\xi}〉 can be transmitted at some rate Q through a noisy channel \ensuremath{\chi} without degradation. We prove that an EPP involving one-way classical communication and acting on mixed state M^(\ensuremath{\chi}) (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel \ensuremath{\chi}) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts ${\mathit{D}}_{1}$(M) and ${\mathit{D}}_{2}$(M) that can be locally distilled from it by EPPs using one- and two-way classical communication, respectively, and give an exact expression for E(M) when M is Bell diagonal. While EPPs require classical communication, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way communication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way communication is available. We exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single-error-correcting quantum block code. We prove that iff a QECC results in high fidelity for the case of no error then the QECC can be recast into a form where the encoder is the matrix inverse of the decoder. \textcopyright{} 1996 The American Physical Society.

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  1. C. H. Bennett, 1996, Phys. Today, 48

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Metadata

Authors
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K.
Affiliations
IBM (United States) (US)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
1996-11-01
Volume
54
Issue
5
Pages
3824-3851
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.54.3824
OpenAlex
W2060887031
Cited by
5,272
References
45
Citations by year
2026: 130 · 2025: 243 · 2024: 247 · 2023: 240 · 2022: 199 · 2021: 224 · 2020: 215 · 2019: 219 · 2018: 163 · 2017: 158 · 2016: 195 · 2015: 159 · 2014: 185 · 2013: 186 · 2012: 181
FWCI
86.14
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • PubMed (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 Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
entanglement distillation, quantum error correction, mixed-state entanglement, Bell-diagonal states, noisy quantum channels, depolarizing channel, universal hashing, two-way classical communication, single-error-correcting codes, quantum state transfer

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