  Finite-density QCD is difficult to study numerically because of the sign
problem. We prove that, in a certain region of the phase diagram, the phase
quenched approximation is exact to O(Nf/Nc). It is true for any physical
observables. We also consider the implications for the lattice simulations and
find a quantitative evidence for the validity of the phase quenching from
existing lattice QCD results at Nc=3. Our results show that the phase-quench
approximation is rather good already at Nc=3, and the 1/Nc correction can be
incorporated by the phase reweighting method without suffering from the overlap
problem. We also show the same equivalence in effective models and holographic
models.
