Polytope compatibility—From quantum measurements to magic squares

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Polytope compatibility—From quantum measurements to magic squares. / Bluhm, Andreas; Nechita, Ion; Schmidt, Simon.

I: Journal of Mathematical Physics, Bind 64, Nr. 12, 122201, 2023.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bluhm, A, Nechita, I & Schmidt, S 2023, 'Polytope compatibility—From quantum measurements to magic squares', Journal of Mathematical Physics, bind 64, nr. 12, 122201. https://doi.org/10.1063/5.0165424

APA

Bluhm, A., Nechita, I., & Schmidt, S. (2023). Polytope compatibility—From quantum measurements to magic squares. Journal of Mathematical Physics, 64(12), [122201]. https://doi.org/10.1063/5.0165424

Vancouver

Bluhm A, Nechita I, Schmidt S. Polytope compatibility—From quantum measurements to magic squares. Journal of Mathematical Physics. 2023;64(12). 122201. https://doi.org/10.1063/5.0165424

Author

Bluhm, Andreas ; Nechita, Ion ; Schmidt, Simon. / Polytope compatibility—From quantum measurements to magic squares. I: Journal of Mathematical Physics. 2023 ; Bind 64, Nr. 12.

Bibtex

@article{0522adfa8f294174be1bebd69e7e5ae4,
title = "Polytope compatibility—From quantum measurements to magic squares",
abstract = "Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its dual). In this article, we generalize this idea and introduce the notion of polytope compatibility, by considering arbitrary polytopes. We find that semiclassical magic squares correspond to Birkhoff polytope compatibility. In general, we prove that polytope compatibility is in one-to-one correspondence with measurement compatibility, when the measurements have some elements in common and the post-processing of the joint measurement is restricted. Finally, we consider how much tuples of operators with appropriate joint numerical range have to be scaled in the worst case in order to become polytope compatible and give both analytical sufficient conditions and numerical ones based on linear programming.",
author = "Andreas Bluhm and Ion Nechita and Simon Schmidt",
note = "Publisher Copyright: {\textcopyright} 2023 Author(s).",
year = "2023",
doi = "10.1063/5.0165424",
language = "English",
volume = "64",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "12",

}

RIS

TY - JOUR

T1 - Polytope compatibility—From quantum measurements to magic squares

AU - Bluhm, Andreas

AU - Nechita, Ion

AU - Schmidt, Simon

N1 - Publisher Copyright: © 2023 Author(s).

PY - 2023

Y1 - 2023

N2 - Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its dual). In this article, we generalize this idea and introduce the notion of polytope compatibility, by considering arbitrary polytopes. We find that semiclassical magic squares correspond to Birkhoff polytope compatibility. In general, we prove that polytope compatibility is in one-to-one correspondence with measurement compatibility, when the measurements have some elements in common and the post-processing of the joint measurement is restricted. Finally, we consider how much tuples of operators with appropriate joint numerical range have to be scaled in the worst case in order to become polytope compatible and give both analytical sufficient conditions and numerical ones based on linear programming.

AB - Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its dual). In this article, we generalize this idea and introduce the notion of polytope compatibility, by considering arbitrary polytopes. We find that semiclassical magic squares correspond to Birkhoff polytope compatibility. In general, we prove that polytope compatibility is in one-to-one correspondence with measurement compatibility, when the measurements have some elements in common and the post-processing of the joint measurement is restricted. Finally, we consider how much tuples of operators with appropriate joint numerical range have to be scaled in the worst case in order to become polytope compatible and give both analytical sufficient conditions and numerical ones based on linear programming.

U2 - 10.1063/5.0165424

DO - 10.1063/5.0165424

M3 - Journal article

AN - SCOPUS:85180563246

VL - 64

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

M1 - 122201

ER -

ID: 377992791