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

Mixed-state entanglement and quantum error correction

Open access
Bennett, Charles H., DiVincenzo, David P., Smolin, John A., Wootters, William K.·1996·Physical Review A
DOI 10.1103/physreva.54.3824
Open this paper in CoChat — free accountOpen PDF

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.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physreva.54.3824

Cites

45 of 45 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The experimental method of measuring the R matrix enables complete determination of steering measures, the fully entangled fraction, and Bell nonlocality measures.

    “This experimental method of measuring the R matrix enables us a complete determination of not only steering measures, but also a fully entangled fraction (FEF)57 and Bell nonlocality measures58.”

    From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [57]

  • Non-maximally entangled states have been shown to reduce the required detector efficiencies for loophole-free tests of Bell inequalities.

    “Non-maximally entangled states have been shown to reduce the required detector efficiencies for loophole-free tests of Bell inequalities [13]”

    From Nonmaximally Entangled States: Production, Characterization, and Utilization (1999) · cites this paper as [13]

    Section 1.2 (p. 4) says that every entangled pure state violates some Bell-type inequality, but it does not discuss detector efficiency. Searches for detector efficiency, detection loopholes, and non-maximally entangled states in Bell tests found no passage addressing whether such states reduce the efficiency required for a loophole-free test. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • Any quantity that is supposed to quantify entanglement needs to be monotonously decreasing under operations that can create or increase only classical correlations.

    “Any quantity that is supposed to quantify entanglement needs to be monotonously decreasing under such operations [25,41].”

    From Measures and dynamics of entangled states (2005) · cites this paper as [41]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. [15][15] M. B. Plenio, V. Vedral and P. L. Knight, 'Optimal Realistic Quantum Error Correction Code', Report No. quant-ph/9603022. - · arXiv
  2. [40][40] E. Knill and R. Laflamme, 'A general theory of quantum error correction codes,' Report No. quant-ph/9604034. - · arXiv

Cited by

Sorted by citations

Related

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 › Computer Science › Artificial Intelligence › 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

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 ›

Are you an author, or do you see a problem with this page? Request a review