  We point out that the quantum Grad's 13-moment system [R. Yano, Physica A:
Statistical Mechanics and its Applications, 416:231-241, 2014] is lack of
global hyperbolicity, and even worse, the thermodynamic equilibrium is not an
interior point of the hyperbolicity region of the system. To remedy this
problem, by fully considering Grad's expansion, we split the expansion into the
equilibrium part and the non-equilibrium part, and propose a regularization for
the system with the help of the new theory developed in [Z. Cai et al., SIAM J.
Appl. Math., 75(5):2001-2023, 2015, Y. Fan, J. Stat. Phys., 161(4), 2015]. This
provides us a new model which is hyperbolic for all admissible thermodynamic
states, and meanwhile preserves the approximate accuracy of the original
system. It should be noted that this procedure is not a trivial application of
the theory in [Z. Cai et al., SIAM J. Appl. Math., 75(5):2001-2023, 2015, Y.
Fan, J. Stat. Phys., 161(4), 2015].
