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The \mathfrak Sk-circular limit of random tensor flattenings

2023/07/21 by Stéphane Dartois, Dartois, Stéphane, Ion Nechita +2
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Probability (math.PR) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2307.11439

openalex publication_date 2023/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint ^*-distribution of the flattenings of large random tensors under mild assumptions, in the sense of free probability theory. We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras for which we describe the covariance structure. As an application we describe the law of large random density matrix of bosonic quantum states.

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