Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators

Andrzej Jamiołkowski, Grzegorz Pastuszak

Assume that $A_1,...,A_s$ are complex $n\times n$ matrices. We give a computable criterion for existence of a common eigenvector of $A_i$ which generalize the result of D. Sh…