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Quantifying measurement incompatibility of mutually unbiased bases

Research output: Contribution to journalArticle

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Quantifying measurement incompatibility of mutually unbiased bases. / Designolle, Sebastien; Skrzypczyk, Paul; Frowis, Florian; Brunner, Nicolas.

In: Physical Review Letters, Vol. 122, 050402, 08.02.2019.

Research output: Contribution to journalArticle

Harvard

Designolle, S, Skrzypczyk, P, Frowis, F & Brunner, N 2019, 'Quantifying measurement incompatibility of mutually unbiased bases' Physical Review Letters, vol. 122, 050402. https://doi.org/10.1103/PhysRevLett.122.050402

APA

Designolle, S., Skrzypczyk, P., Frowis, F., & Brunner, N. (2019). Quantifying measurement incompatibility of mutually unbiased bases. Physical Review Letters, 122, [050402]. https://doi.org/10.1103/PhysRevLett.122.050402

Vancouver

Designolle S, Skrzypczyk P, Frowis F, Brunner N. Quantifying measurement incompatibility of mutually unbiased bases. Physical Review Letters. 2019 Feb 8;122. 050402. https://doi.org/10.1103/PhysRevLett.122.050402

Author

Designolle, Sebastien ; Skrzypczyk, Paul ; Frowis, Florian ; Brunner, Nicolas. / Quantifying measurement incompatibility of mutually unbiased bases. In: Physical Review Letters. 2019 ; Vol. 122.

Bibtex

@article{26a7cda7ebd94a5595a7b68ccdafc7c7,
title = "Quantifying measurement incompatibility of mutually unbiased bases",
abstract = "Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d+ 1 MUB (given d is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.",
author = "Sebastien Designolle and Paul Skrzypczyk and Florian Frowis and Nicolas Brunner",
year = "2019",
month = "2",
day = "8",
doi = "10.1103/PhysRevLett.122.050402",
language = "English",
volume = "122",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society (APS)",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Quantifying measurement incompatibility of mutually unbiased bases

AU - Designolle, Sebastien

AU - Skrzypczyk, Paul

AU - Frowis, Florian

AU - Brunner, Nicolas

PY - 2019/2/8

Y1 - 2019/2/8

N2 - Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d+ 1 MUB (given d is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.

AB - Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d+ 1 MUB (given d is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.

UR - https://arxiv.org/abs/1805.09609

U2 - 10.1103/PhysRevLett.122.050402

DO - 10.1103/PhysRevLett.122.050402

M3 - Article

VL - 122

JO - Physical Review Letters

T2 - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

M1 - 050402

ER -