Abstract
We theoretically investigate the phase sensitivity with parity detection on a Mach–Zehnder interferometer with a coherent state combined with a photon-added squeezed vacuum state. Our results show that when the phase shift to be estimated approaches zero, the squeezed vacuum state is indeed the optimal state within a constraint on the average photon number. However, when the phase shift slightly deviates from zero, in terms of parity detection, the photon-added squeezed vacuum state can give the better phase sensitivity than both the squeezed vacuum state and the photon-subtracted squeezed vacuum state when these interferometer states carry many photons. In addition, we also show that the quantum Cramér–Rao bound can be reached by parity detection when the phase shift approaches zero.
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