hi,
if you mean how a general density matrix is invariant under unitary transformation, the consider that density matrices are used to evaluate mean values of an operator A, <A R>= Tr(AR), where R is the density matrix and Tr denotes the trace operation. Then performing a unitary transformation...
Hello,
Schmidt decomposition is a usefull tool for bipartite systems: if it admits a decomposition with more than one Schmidt coefficient, then the overall state is an entangled one. So every bipartite state has a Schmidt decomposition, but only if it's entangles there's more than one...