Quantum Compression Relative to a Set of Measurements

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Standard

Quantum Compression Relative to a Set of Measurements. / Bluhm, Andreas; Rauber, Lukas; Wolf, Michael M.

I: Annales Henri Poincare, Bind 19, Nr. 6, 01.06.2018, s. 1891-1937.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bluhm, A, Rauber, L & Wolf, MM 2018, 'Quantum Compression Relative to a Set of Measurements', Annales Henri Poincare, bind 19, nr. 6, s. 1891-1937. https://doi.org/10.1007/s00023-018-0660-z

APA

Bluhm, A., Rauber, L., & Wolf, M. M. (2018). Quantum Compression Relative to a Set of Measurements. Annales Henri Poincare, 19(6), 1891-1937. https://doi.org/10.1007/s00023-018-0660-z

Vancouver

Bluhm A, Rauber L, Wolf MM. Quantum Compression Relative to a Set of Measurements. Annales Henri Poincare. 2018 jun. 1;19(6):1891-1937. https://doi.org/10.1007/s00023-018-0660-z

Author

Bluhm, Andreas ; Rauber, Lukas ; Wolf, Michael M. / Quantum Compression Relative to a Set of Measurements. I: Annales Henri Poincare. 2018 ; Bind 19, Nr. 6. s. 1891-1937.

Bibtex

@article{2b6d241e22654004999bd6480ac894c3,
title = "Quantum Compression Relative to a Set of Measurements",
abstract = "In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of classical side information. We find that the latter can be bounded, which implies that the minimal compression dimension is stable in the sense that it cannot be decreased by allowing for small errors. Various bounds on the minimal compression dimension are proven, and an SDP-based algorithm for its computation is provided. The results are based on two independent approaches: an operator algebraic method using a fixed-point result by Arveson and an algebro-geometric method that relies on irreducible polynomials and B{\'e}zout{\textquoteright}s theorem. The latter approach allows lifting the results from the single-copy level to the case of multiple copies and from completely positive to merely positive maps.",
author = "Andreas Bluhm and Lukas Rauber and Wolf, {Michael M.}",
year = "2018",
month = jun,
day = "1",
doi = "10.1007/s00023-018-0660-z",
language = "English",
volume = "19",
pages = "1891--1937",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Springer Basel AG",
number = "6",

}

RIS

TY - JOUR

T1 - Quantum Compression Relative to a Set of Measurements

AU - Bluhm, Andreas

AU - Rauber, Lukas

AU - Wolf, Michael M.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of classical side information. We find that the latter can be bounded, which implies that the minimal compression dimension is stable in the sense that it cannot be decreased by allowing for small errors. Various bounds on the minimal compression dimension are proven, and an SDP-based algorithm for its computation is provided. The results are based on two independent approaches: an operator algebraic method using a fixed-point result by Arveson and an algebro-geometric method that relies on irreducible polynomials and Bézout’s theorem. The latter approach allows lifting the results from the single-copy level to the case of multiple copies and from completely positive to merely positive maps.

AB - In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of classical side information. We find that the latter can be bounded, which implies that the minimal compression dimension is stable in the sense that it cannot be decreased by allowing for small errors. Various bounds on the minimal compression dimension are proven, and an SDP-based algorithm for its computation is provided. The results are based on two independent approaches: an operator algebraic method using a fixed-point result by Arveson and an algebro-geometric method that relies on irreducible polynomials and Bézout’s theorem. The latter approach allows lifting the results from the single-copy level to the case of multiple copies and from completely positive to merely positive maps.

UR - http://www.mendeley.com/research/quantum-compression-relative-set-measurements

U2 - 10.1007/s00023-018-0660-z

DO - 10.1007/s00023-018-0660-z

M3 - Journal article

VL - 19

SP - 1891

EP - 1937

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 6

ER -

ID: 231872560