The tensor Harish-Chandra--Itzykson--Zuber integral II: detecting entanglement in large quantum systems

TL;DR

This paper extends the Harish-Chandra--Itzykson--Zuber integral to tensors, analyzing its asymptotic behavior for large tensor sizes, with implications for understanding entanglement in multipartite quantum systems.

Contribution

It introduces a tensor generalization of the integral and explores its asymptotic regimes, advancing the analysis of quantum entanglement properties.

Findings

Identified multiple non-trivial asymptotic regimes.

Analyzed the behavior under various scaling assumptions.

Discussed applications to quantum entanglement detection.

Abstract

We consider the recently introduced generalization of the Harish-Chandra--Itzykson--Zuber integral to tensors and discuss its asymptotic behavior when the characteristic size N of the tensors is taken to be large. This study requires us to make assumptions on the scaling with N of the external tensors. We analyze a two-parameter class of asymptotic scaling ans\"{a}tze, uncovering several non-trivial asymptotic regimes. This study is relevant for analyzing the entanglement properties of multipartite quantum systems. We discuss potential applications of our results to this domain, in particular in the context of randomized local measurements.