Quantum marginal problem and representations of the symmetric group

2004/09/17 by Alexander A. Klyachko, Alexander Klyachko, Klyachko, Alexander · 11 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph) #Random Matrices and Applications #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0409113

AMS-LaTeX version 2.08, 47 pages

arxiv created 2004/09/17 · openalex publication_date 2004/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive tables of marginal inequalities, including arrays up to 4 qubits. In the second part of the paper we pursue another approach based on reduction of the problem to representation theory of the symmetric group.

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