Quantum interferometry via a coherent state mixed with a photon-added squeezed vacuum state

TL;DR

This paper theoretically explores phase sensitivity in a Mach-Zehnder interferometer using a coherent state combined with a photon-added squeezed vacuum state, demonstrating optimal states and the attainability of the quantum Cramér-Rao bound.

Contribution

It identifies the photon-added squeezed vacuum state as optimal for phase estimation near zero phase shift and shows that parity detection can reach the quantum Cramér-Rao bound.

Findings

Photon-added squeezed vacuum state is optimal near zero phase shift.

Parity detection can reach the quantum Cramér-Rao bound.

Optimality depends on the phase shift and photon number.

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. When the phase shift approaches zero, the squeezed vacuum state is indeed the optimal state within a constraint on the average number of photons. However, when the phase shift to be estimated slightly deviates from zero, the optimal state is neither the squeezed vacuum state nor the photon-subtracted squeezed vacuum state, but the photon-added squeezed vacuum state when they carry many photons. Finally, we show that the quantum Cram\'{e}r-Rao bound can be reached by parity detection.