The Wigner-Yanase entropy is not subadditive
arXiv:math-ph/0609019 · doi:10.1007/s10955-006-9265-x
Abstract
Wigner and Yanase introduced in 1963 the Wigner-Yanase entropy defined as minus the skew information of a state with respect to a conserved observable. They proved that the Wigner-Yanase entropy is a concave function in the state and conjectured that it is subadditive with respect to the aggregation of possibly interacting subsystems. While this turned out to be true for the quantum-mechanical entropy, we negate the conjecture for the Wigner-Yanase entropy by providing a counter example.
To appear in Journal of Statistical Physics