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.

中文翻译：

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使用具有非整数q值的Lambert-Tsallis W _q函数计算Wigner函数的熵

Wigner函数是一种数学工具，可提供有关量子光状态的重要信息，例如纠缠和量子度。例如，在最近的工作中，证明了使用Lambert–Tsallis $ {W_q} $函数和$ q = {2} $的Wigner函数的熵可以用作量子度的度量。当$ q $的值不是整数时，熵和$ {W_q} $函数具有分数次方，因此，维格纳函数的负值可能会导致熵的复数值。这禁止在计算高度感兴趣的状态（如薛定ding猫）的维格纳函数的熵时使用这些函数。为了克服这个问题，我们提出了一个受Rényi熵启发的新的熵方程。讨论了这种新的熵的优缺点，并给出了数值示例。