The Wigner-Yanase entropy is not subadditive

TL;DR

This paper disproves the long-standing conjecture that the Wigner-Yanase entropy is subadditive, providing a counterexample that challenges previous assumptions about its properties in quantum information theory.

Contribution

The paper demonstrates that the Wigner-Yanase entropy is not subadditive by constructing a specific counterexample, refuting a conjecture from quantum information theory.

Findings

Counterexample shows non-subadditivity of Wigner-Yanase entropy

Challenges previous assumptions about entropy properties

Impacts understanding of quantum entropy measures

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.