2004/09/30 by Matthias Christandl, Graeme Mitchison · 3 citations
Physics and Astronomy · #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1007/s00220-005-1435-1
published as Commun. Math. Phys., Vol. 261, No. 3, pp. 789-797 (2006) · 5 pages, v2 minor changes
openalex publication_date 2005/10/18 · arxiv created 2006/02/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can associate a representation of the symmetric group defined by a Young diagram whose normalised row lengths approximate the spectrum. We show that, for allowed spectra, the representation of the composite system is contained in the tensor product of the representations of the two subsystems. This gives a new physical meaning to representations of the symmetric group. It also introduces a new way of using the machinery of group theory in quantum informational problems, which we illustrate by two simple examples.