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.
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