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

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

By Angela Capel

Appears in 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.

Information about the video

Date of recording 09/07/2024
Date of publication 26/07/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20199803
Cite this video 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

Domain(s)

Quantum Physics

Bibliography

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

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