Optimal decompositions with respect to entropy and symmetries
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.
optimal decompositions for three-level systems
scientific article; zbMATH DE number 1331408