Berlin 2005 – scientific programme

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Q: Quantenoptik und Photonik

Q 67: Quanteninformation IV

Q 67.6: Talk

Wednesday, March 9, 2005, 12:15–12:30, HU 2002

The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group — •Matthias Christandl and Graeme Mitchison — Centre for Quantum Computation, University of Cambridge

Consider triples of spectra corresponding to a density matrix on a bipartite system and its two subsystems. We show that, for every such triple, certain Kronecker coefficients of the symmetric group must be non-zero. These coefficients correspond to triples of Young diagrams whose distribution of row lengths approximate the spectra. This makes a connection between properties of operators and a flourishing area of group representation theory. As a simple illustration we give a novel proof of subadditivity of von Neumann entropy and the Araki-Lieb inequality.