Quantum marginal problem and representations of the symmetric group
arXiv:quant-ph/0409113
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.
AMS-LaTeX version 2.08, 47 pages