Abstract: Some quantum entropy，such as von Neumann entropy，linear entropy，Rényi entropy，Tsallis entropy，

and several different definitions of them based on Wigner functions in phase space，are introduced respectively.

Through some theoretical deductions and numerical calculations，the definitions of quantum entropy in phase

space using the absolute value of Wigner function in the literatures are proved to be inappropriate. The quantum entropy

defined in this paper by the Moyal star product of Wigner function is consistent with that defined by density

　　matrices.

Key words: Wigner function, von Neumann entropy, Tsallis entropy, Rényi entropy, linear entropy