Jean Morlet Chair - Research school: Random quantum channels: entanglement and entropies / Chaire Jean Morlet - Ecole: Canaux quantiques aléatoires: Intrication et entropies

Collection Jean Morlet Chair - Research school: Random quantum channels: entanglement and entropies / Chaire Jean Morlet - Ecole: Canaux quantiques aléatoires: Intrication et entropies

Organisateur(s) Collins, Benoît ; Demni, Nizar ; Kadri, Hachem ; Lancien, Cécilia ; Nechita, Ion ; Pellegrini, Clément

Date(s) 08/07/2024 - 12/07/2024

URL associée https://conferences.cirm-math.fr/3051.html

00:00:00 / 00:00:00

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Interpolation between random matrices and free operators, and application to Quantum Information Theory

De Félix Parraud

One of the most important question in Quantum Information Theory was to figure out whether the so-called Minimum Output Entropy (MOE) was additive. In this talk I will start by defining the counter-example originally built by Belinschi, Collins and Nechita. Then I will explain how with the help of a novel strategy, we managed with Collins to compute concentration estimate on the probability that the MOE is non-additive and how it yielded some explicit bounds for the dimension of spaces where violation of the MOE occurs. Finally, I will talk more in detail about this novel strategy which consists in interpolating random matrices and free operators with the help of free stochastic calculus.

Informations sur la vidéo

Date de captation 08/07/2024
Date de publication 26/07/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20200403
Citer cette vidéo Parraud, Félix (08/07/2024). Interpolation between random matrices and free operators, and application to Quantum Information Theory. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20200403
URL https://dx.doi.org/10.24350/CIRM.V.20200403

Domaine(s)

Bibliographie

PARRAUD, Félix. On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices. Probability Theory and Related Fields, 2022, vol. 182, no 3, p. 751-806. - http://dx.doi.org/10.1007/s00440-021-01101-0
COLLINS, Benoît et PARRAUD, Félix. Concentration estimates for random subspaces of a tensor product and application to quantum information theory. Journal of Mathematical Physics, 2022, vol. 63, no 10. - https://doi.org/10.1063/5.0073837
PARRAUD, Félix. Asymptotic expansion of smooth functions in deterministic and iid Haar unitary matrices, and application to tensor products of matrices. arXiv preprint arXiv:2302.02943, 2023. - https://doi.org/10.48550/arXiv.2302.02943

Codes MSC

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