Polytope compatibility - from quantum measurements to magic squares

Publikation: Working paper › Preprint › Forskning

Standard

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

arXiv preprint, 2023.

Publikation: Working paper › Preprint › Forskning

Harvard

Bluhm, A, Nechita, I & Schmidt, S 2023 'Polytope compatibility - from quantum measurements to magic squares' arXiv preprint.

APA

Bluhm, A., Nechita, I., & Schmidt, S. (2023). Polytope compatibility - from quantum measurements to magic squares. arXiv preprint.

Vancouver

Bluhm A, Nechita I, Schmidt S. Polytope compatibility - from quantum measurements to magic squares. arXiv preprint. 2023.

Author

Bluhm, Andreas ; Nechita, Ion ; Schmidt, Simon. / Polytope compatibility - from quantum measurements to magic squares. arXiv preprint, 2023.

Bibtex

@techreport{c6465496f14f4da5b9b3fe46c7cd0af9,
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 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",
year = "2023",
language = "English",
publisher = "arXiv preprint",
type = "WorkingPaper",
institution = "arXiv preprint",

}

RIS

TY - UNPB

T1 - Polytope compatibility - from quantum measurements to magic squares

AU - Bluhm, Andreas

AU - Nechita, Ion

AU - Schmidt, Simon

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 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 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.

M3 - Preprint

BT - Polytope compatibility - from quantum measurements to magic squares

PB - arXiv preprint

ER -

ID: 346259563