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The tensor Harish-Chandra-Itzykson-Zuber integral
Multi angle
Authors : Gurău, Răzvan (Author of the conference)
CIRM (Publisher )
05A15 - Exact enumeration problems, generating functions
81P99 - None of the above but in this section
60C99 - None of the above, but in this section
CIRM (Publisher )
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Abstract :
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.
Keywords : Weingarten calculus; random tensor
MSC Codes : Keywords : Weingarten calculus; random tensor
05A15 - Exact enumeration problems, generating functions
81P99 - None of the above but in this section
60C99 - None of the above, but in this section
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/03/2022 Conference Date : 17/03/2022 Subseries : Research talks arXiv category : Mathematical Physics ; Dynamical Systems Mathematical Area(s) : Combinatorics ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:49:18 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2022-03-17_Gurau.mp4 
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Information on the Event
Event Title : Random Tensors / Tenseurs aléatoiresEvent Organizers : Dartois, Stéphane ; De las Cuevas, Gemma ; Lancien, Cécilia ; Lionni, Luca ; Nechita, Ion Dates : 14/03/2022 - 18/03/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2541.html
Citation Data
DOI : 10.24350/CIRM.V.19896503Cite this video as: Gurău, Răzvan (2022). The tensor Harish-Chandra-Itzykson-Zuber integral. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19896503 URI : http://dx.doi.org/10.24350/CIRM.V.19896503 |
See Also
- [Multi angle] Tensor networks for quantum many-body systems - lecture 2 / Author of the conference Bañuls, Mari Carmen.
- [Multi angle] Tensor PCA / Author of the conference Ben Arous, Gérard.
- [Multi angle] Tensor networks for quantum many-body systems - lecture 1 / Author of the conference Bañuls, Mari Carmen.
- [Multi angle] Asymptotic tensor powers of Banach spaces / Author of the conference Aubrun, Guillaume.
- [Multi angle] Approximation and learning with tree tensor networks - lecture 2 / Author of the conference Nouy, Anthony.
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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