Wehrl entropy

In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi-entropy defined for the Husimi Q representation of the phase-space quasiprobability distribution. See for a comprehensive review of basic properties of classical, quantum and Wehrl entropies, and their implications in statistical mechanics. In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi-entropy defined for the Husimi Q representation of the phase-space quasiprobability distribution. See for a comprehensive review of basic properties of classical, quantum and Wehrl entropies, and their implications in statistical mechanics. The Husimi function is a 'classical phase-space' function of position x and momentum p, and in one dimension is defined for any quantum-mechanical density matrix ρ by where φ is a '(Glauber) coherent state', given by (It can be understood as the Weierstrass transform of the Wigner quasi-probability distribution.) The Wehrl entropy is then defined as