A generic quantum Wielandt's inequality for matrix and Lie algebras | Vidéo | Carmin.tv

00:00:00 / 00:00:00

A generic quantum Wielandt's inequality for matrix and Lie algebras

De Angela Capel

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

Here, we provide a generic version of quantum Wielandt's inequality, which gives an optimal upper bound on the minimal length such that products of that length of n-dimensional matrices in a generating system span the whole matrix algebra with probability one. This length generically is of order $\Theta(\log n)$, as opposed to the general case, in which the best bound is $O(n^2)$. This has implications for the primitivity index of random quantum channels, matrix product states and projected entangled pair states. Some results can be extended to Lie algebras. Joint work with Yifan Jia.

Informations sur la vidéo

Date de captation 09/07/2024
Date de publication 26/07/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20199803
Citer cette vidéo Capel, Angela (09/07/2024). A generic quantum Wielandt's inequality for matrix and Lie algebras. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20199803
URL https://dx.doi.org/10.24350/CIRM.V.20199803

Domaine(s)

Physique quantique

Bibliographie

JIA, Yifan et CAPEL, Angela. A generic quantum Wielandt's inequality. Quantum, 2024, vol. 8, p. 1331. - https://doi.org/10.22331/q-2024-05-02-1331

Codes MSC

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2026

Donner son avis