Further results on entropy and separability
Yuan Li, Yue Wang · Journal of Physics A Mathematical and Theoretical · 2012
Let Φ be a bi-stochastic quantum operation. We obtain that S(Φ(ρ)) = S(ρ) for any quantum state ρ if and only if there exists a unitary operator U such that Φ(ρ) = UρU†, that is, Φ is a unitary operation. It is well known that a bipartite quantum state ρAB is separable if and only if it can be written as ρAB = ∑iλi|φi〉〈φi|⊗|ψi〉〈ψi|, where ∑iλi = 1, |φi〉 and |ψi〉 are the normalized pure states of the subsystems and respectively, which may not be orthogonal in general. In this paper, we also present some necessary and sufficient conditions for which the sets |φi〉 are orthonormal vectors.