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We show that the phase sensitivity of a Mach-Zehnder interferometer illuminated by a coherent state in one input port and a squeezed-vacuum state in the other port is (i) independent of the true value of the phase shift and (ii) can reach the Heisenberg limit 1/Nₓ, where Nₓ is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, 0ex{0ex}1/|{|^2e^2r+sinh^2r}, can be saturated for arbitrary values of the squeezing parameter r and the amplitude of the coherent mode by using a Bayesian phase inference protocol.
Pezzè et al. (Tue,) studied this question.