1. The problem statement, all variables and given/known data Given a matrix M(a) = (a -(1/4)i ; (1/4)i a) (semicolon separates rows) a) Determine a so that M(a) is a density matrix. b) Show that the system is in a mixed state. c) Purify M(a) 3. The attempt at a solution a) from conditions for a density matrices 1) M(a)=M(a)* 2) tr(M(a))=1 3) M(a)>=0 form 1) a must be real from 2) a=1/2 I'm not sure what 3) means, but if it means trace and determinant must be non-negative, than this is also fulfilled if a=1/2. b) I think that condition for system to be in mixed state is: M(a)^2 /= M(a) since this is true for M(a), system is in mixed state. c) Don't know how to solve this part, Maybe it has to do something with decomposing a matrix ?