Bounds for disentropy of the Wigner function

James Gareth Wood

Anthony J. Bracken, Demosthenes Ellinas, James Gareth Wood

Demosthenes Ellinas, I. Tsohantjis

Rubens Viana Ramos

In this work, the usage of the disentropy of the Wigner function as order and quantumness measure is investigated. Furthermore, the relative disentropy of the Wigner function as a distance measure between two Wigner functions is also discussed. The numerical calculation of the dynamic of the disentropy and relative disentropy of the Wigner function are realized considering an initially pure quantum state that evolves to a classical mixture and when an initially coherent state evolves to a Schrödinger cat state. It is shown that in all cases the disentropy is minimal for the quantum states with maximal quantumness, and it is maximal for maximally ordered states (pure states with positive Wigner function).

José leonardo Esteves da Silva, Rubens Viana Ramos

The Wigner function is a mathematical tool that provides important information about a quantum light state, like entanglement and quantumness. For example, in a recent work it was shown the disentropy of the Wigner function using the Lambert–Tsallis W q function with q = 2 can be used as a measure of quantumness. When the value of q is non-integer, the disentropy and W q function have fractional powers and, hence, a negative value of the Wigner function can result in a complex value for the disentropy. This prohibits the use of those functions in the calculation of the disentropy of the Wigner function of highly interesting states, such as Schrödinger cats. In order to overcome this problem, we propose a new disentropy equation inspired by the Rényi entropy. The advantages and disadvantages of this new disentropy are discussed and numerical examples are shown.

R. Ramanathan