  A minimum uncertainty state for position and momentum is obtained in quantum
viscous hydrodynamics which is defined through the Navier-Stokes-Korteweg (NSK)
equation. This state is the generalization of the coherent state and its
uncertainty is given by a function of the coefficient of viscosity. The
uncertainty can be smaller than the standard minimum value in quantum
mechanics, $\hbar/2$, when the coefficient of viscosity is smaller than a
critical value which is similar in magnitude to the Kovtun-Son-Starinets (KSS)
bound.
