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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.

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Citation data

  • DOI 10.24350/CIRM.V.19896503
  • Cite this video GURAU Razvan (3/17/22). 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


  • 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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