Communications in Mathematical Physics

, Volume 261, Issue 3, pp 789–797 | Cite as

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

  • Matthias ChristandlEmail author
  • Graeme Mitchison


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum State 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Centre for Quantum Computation, Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUnited Kingdom
  2. 2.MRC Laboratory of Molecular BiologyUniversity of CambridgeCambridgeUnited Kingdom

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