The $\mathfrak S_k$-circular limit of random tensor flattenings
hal.structure.identifier | Laboratoire d'Intégration des Systèmes et des Technologies [LIST (CEA)] | |
dc.contributor.author | DARTOIS, Stéphane | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | MALE, Camille | |
hal.structure.identifier | Laboratoire de Physique Théorique [LPT] | |
hal.structure.identifier | Cohérence Quantique (LPT) [ICQ] | |
dc.contributor.author | NECHITA, Ion | |
dc.date.accessioned | 2024-04-04T02:33:29Z | |
dc.date.available | 2024-04-04T02:33:29Z | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190484 | |
dc.description.abstractEn | 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. | |
dc.language.iso | en | |
dc.title.en | The $\mathfrak S_k$-circular limit of random tensor flattenings | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
dc.subject.hal | Physique [physics]/Physique Quantique [quant-ph] | |
dc.identifier.arxiv | 2307.11439 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-04179139 | |
hal.version | 1 | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-04179139v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DARTOIS,%20St%C3%A9phane&MALE,%20Camille&NECHITA,%20Ion&rft.genre=preprint |
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