On the failure of subadditivity of the Wigner-Yanase entropy
Robert Seiringer
It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample. In 1963, Wigner and Yanase [4] introduced the entropy-like quantity S WY (ρ, K) = 1 2 Tr[ρ1/2, K] 2 = Trρ 1/2 Kρ 1/2 K − TrρK 2 for density matrices ρ of quantum systems, with K some fixed self-adjoint operator. They showed that S WY is concave in ρ [4, 5] and, for pure states, subadditive with respect to decomposition of the quantum system into two subsystems.
•Jan 1, 2007•5 citations