Compatibility of quantum measurements and inclusion constants for the matrix jewel

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Compatibility of quantum measurements and inclusion constants for the matrix jewel. / Bluhm, Andreas; Nechita, Ion.

In: SIAM Journal on Applied Algebra and Geometry, Vol. 4, No. 2, 2020, p. 255-296.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bluhm, A & Nechita, I 2020, 'Compatibility of quantum measurements and inclusion constants for the matrix jewel', SIAM Journal on Applied Algebra and Geometry, vol. 4, no. 2, pp. 255-296. https://doi.org/10.1137/19M123837X

APA

Bluhm, A., & Nechita, I. (2020). Compatibility of quantum measurements and inclusion constants for the matrix jewel. SIAM Journal on Applied Algebra and Geometry, 4(2), 255-296. https://doi.org/10.1137/19M123837X

Vancouver

Bluhm A, Nechita I. Compatibility of quantum measurements and inclusion constants for the matrix jewel. SIAM Journal on Applied Algebra and Geometry. 2020;4(2):255-296. https://doi.org/10.1137/19M123837X

Author

Bluhm, Andreas ; Nechita, Ion. / Compatibility of quantum measurements and inclusion constants for the matrix jewel. In: SIAM Journal on Applied Algebra and Geometry. 2020 ; Vol. 4, No. 2. pp. 255-296.

Bibtex

@article{9c47ef84069f4c93bbab67d269c8c6c2,
title = "Compatibility of quantum measurements and inclusion constants for the matrix jewel",
abstract = "In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.",
keywords = "Algebraic convexity, Free spectrahedra, Polytope, Quantum cloning, Quantum measurement, Semidefinite relaxation",
author = "Andreas Bluhm and Ion Nechita",
year = "2020",
doi = "10.1137/19M123837X",
language = "English",
volume = "4",
pages = "255--296",
journal = "SIAM Journal on Applied Algebra and Geometry",
issn = "2470-6566",
publisher = "Society for Industrial and Applied Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - Compatibility of quantum measurements and inclusion constants for the matrix jewel

AU - Bluhm, Andreas

AU - Nechita, Ion

PY - 2020

Y1 - 2020

N2 - In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.

AB - In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.

KW - Algebraic convexity

KW - Free spectrahedra

KW - Polytope

KW - Quantum cloning

KW - Quantum measurement

KW - Semidefinite relaxation

UR - https://www.mendeley.com/catalogue/801c874a-45ec-361e-9930-3422d49469ac/

U2 - 10.1137/19M123837X

DO - 10.1137/19M123837X

M3 - Journal article

VL - 4

SP - 255

EP - 296

JO - SIAM Journal on Applied Algebra and Geometry

JF - SIAM Journal on Applied Algebra and Geometry

SN - 2470-6566

IS - 2

ER -

ID: 255789501