Optimal decompositions with respect to entropy and symmetries (Q1300953)

Research on quantum ergodic theory to some extend is fueled by recent progress in quantum computation and the observation that the ``degree of quantum entanglement'' is controlled and measured by the ``entropy of a subalgebra''. In their letter, the authors extend results previously obtained on the optimal (with respect to entropy of some abelian subalgebra) decompositions for three-level systems which may prove central to quantum information. The class of three-dimensional state spaces is enlarged by allowing now for complex symmetric density matrices parametrized by two real parameters. For the most part, calculations are done analytically. However, a supplementary numerical study seemed to be unavoidable. In their final chapter, the authors discuss to what extent optimal decompositions of generic \(3\times 3\) density matrices can be controlled.