The Spectra of Quantum States and the Kronecker Coefficients of the Symmetric Group

By Matthias Christandl, Graeme J. Mitchison. 2004

145 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/767b72ee92110f56db7b614349c96dccb87fddeb

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Sample-Optimal Tomography of Quantum States (2015, methodology): “Here, the optimal covariant measurement was described by Keyl and Werner [26], its large-deviation properties were derived in [27] (see also [28]), and it was analyzed further in [29, 30].”
Nonzero Kronecker Coefficients and What They Tell us about Spectra (2007, methodology): “In [ 4 ], the approach came from the direction of quantum information theory, and a key ingredient was a theorem relating spectra and Young diagrams due to Alicki, Rudnicki and Sadowski [16] and Keyl and Werner [11].”