Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms

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Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms. / Bluhm, Andreas; Jenčová, Anna; Nechita, Ion.

I: Communications in Mathematical Physics, Bind 393, 08.2022, s. 1125–1198.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bluhm, A, Jenčová, A & Nechita, I 2022, 'Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms', Communications in Mathematical Physics, bind 393, s. 1125–1198. https://doi.org/10.48550/arXiv.2011.06497, https://doi.org/10.1007/s00220-022-04379-w

APA

Bluhm, A., Jenčová, A., & Nechita, I. (2022). Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms. Communications in Mathematical Physics, 393, 1125–1198. https://doi.org/10.48550/arXiv.2011.06497, https://doi.org/10.1007/s00220-022-04379-w

Vancouver

Bluhm A, Jenčová A, Nechita I. Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms. Communications in Mathematical Physics. 2022 aug.;393:1125–1198. https://doi.org/10.48550/arXiv.2011.06497, https://doi.org/10.1007/s00220-022-04379-w

Author

Bluhm, Andreas ; Jenčová, Anna ; Nechita, Ion. / Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms. I: Communications in Mathematical Physics. 2022 ; Bind 393. s. 1125–1198.

Bibtex

@article{be5980d169ee4754a89f2369eda2e44a,
title = "Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms",
abstract = "In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is in terms of the positivity of associated maps. The second relates compatibility to the inclusion of certain generalized spectrahedra. For this, we extend the theory of free spectrahedra to ordered vector spaces. The third characterization connects the compatibility of dichotomic measurements to the ratio of tensor crossnorms of Banach spaces. We use these characterizations to study the amount of incompatibility present in different GPTs, i.e. their compatibility regions. For centrally symmetric GPTs, we show that the compatibility degree is given as the ratio of the injective and the projective norm of the tensor product of associated Banach spaces. This allows us to completely characterize the compatibility regions of several GPTs, and to obtain optimal universal bounds on the compatibility degree in terms of the 1-summing constants of the associated Banach spaces. Moreover, we find new bounds on the maximal incompatibility present in more than three qubit measurements.",
author = "Andreas Bluhm and Anna Jen{\v c}ov{\'a} and Ion Nechita",
year = "2022",
month = aug,
doi = "10.48550/arXiv.2011.06497",
language = "English",
volume = "393",
pages = "1125–1198",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms

AU - Bluhm, Andreas

AU - Jenčová, Anna

AU - Nechita, Ion

PY - 2022/8

Y1 - 2022/8

N2 - In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is in terms of the positivity of associated maps. The second relates compatibility to the inclusion of certain generalized spectrahedra. For this, we extend the theory of free spectrahedra to ordered vector spaces. The third characterization connects the compatibility of dichotomic measurements to the ratio of tensor crossnorms of Banach spaces. We use these characterizations to study the amount of incompatibility present in different GPTs, i.e. their compatibility regions. For centrally symmetric GPTs, we show that the compatibility degree is given as the ratio of the injective and the projective norm of the tensor product of associated Banach spaces. This allows us to completely characterize the compatibility regions of several GPTs, and to obtain optimal universal bounds on the compatibility degree in terms of the 1-summing constants of the associated Banach spaces. Moreover, we find new bounds on the maximal incompatibility present in more than three qubit measurements.

AB - In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is in terms of the positivity of associated maps. The second relates compatibility to the inclusion of certain generalized spectrahedra. For this, we extend the theory of free spectrahedra to ordered vector spaces. The third characterization connects the compatibility of dichotomic measurements to the ratio of tensor crossnorms of Banach spaces. We use these characterizations to study the amount of incompatibility present in different GPTs, i.e. their compatibility regions. For centrally symmetric GPTs, we show that the compatibility degree is given as the ratio of the injective and the projective norm of the tensor product of associated Banach spaces. This allows us to completely characterize the compatibility regions of several GPTs, and to obtain optimal universal bounds on the compatibility degree in terms of the 1-summing constants of the associated Banach spaces. Moreover, we find new bounds on the maximal incompatibility present in more than three qubit measurements.

U2 - 10.48550/arXiv.2011.06497

DO - 10.48550/arXiv.2011.06497

M3 - Journal article

VL - 393

SP - 1125

EP - 1198

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -

ID: 333053263