Von Neumann entropy-preserving quantum operations

For a given quantum state rho and two quantum operations phi and psi, the information encoded in the quantum state rho is quantified by its von Neumann entropy S(rho). By the famous Choi-Jamiotkowski isomorphism, the quantum operation phi can be transformed into a bipartite state, the von Neumann entropy S-map(phi) of the bipartite state describes the decoherence induced by phi. In this Letter, we characterize not only the pairs (phi, rho) which satisfy S(phi(rho)) = S(rho), but also the pairs (phi, psi) which satisfy S-map(phi circle psi) = S-map(psi). (C) 2011 Elsevier B.V. All rights reserved.