The tensor Harish-Chandra-Itzykson-Zuber integral | Vidéo | Carmin.tv

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The tensor Harish-Chandra-Itzykson-Zuber integral

By Razvan Gurau

Appears in collection : Random Tensors / Tenseurs aléatoires

I will present some recent results concerning the generalization of the Harish-ChandraItzykson-Zuber integral to the case where the group integrated over is not UpN Dq, but the subgroup UpNq bD. This case is relevant for the study of D-partite quantum systems. While the HCIZ integral can no longer be expressed in terms of eigenvalues of the source matrices, it can be explicitly computed using Weingarten calculus. This result allows us to formulate a criterion for the detection of entanglement in multipartite quantum systems, which I will discuss in some detail.

Information about the video

Date of recording 17/03/2022
Date of publication 29/03/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19896503
Cite this video GURAU, Razvan (17/03/2022). The tensor Harish-Chandra-Itzykson-Zuber integral. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19896503
URL https://dx.doi.org/10.24350/CIRM.V.19896503

Domain(s)

Bibliography

COLLINS, Benoît, GURAU, Razvan, et LIONNI, Luca. The tensor Harish-Chandra--Itzykson--Zuber integral II: detecting entanglement in large quantum systems. arXiv preprint arXiv:2201.12778, 2022. - https://arxiv.org/abs/2201.12778
COLLINS, Benoît, GURAU, Razvan, et LIONNI, Luca. The tensor Harish-Chandra-Itzykson-Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers. arXiv preprint arXiv:2010.13661, 2020. - https://arxiv.org/abs/2010.13661

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