Enhanced interferometry using squeezed thermal states and even or odd states

TL;DR

This paper derives a general quantum Fisher information expression for Mach-Zehnder interferometers with arbitrary pure states and squeezed thermal states, showing that even or odd states can surpass the standard quantum limit and approach the Heisenberg limit.

Contribution

It introduces a general framework for quantum Fisher information in interferometry with arbitrary pure states and squeezed thermal states, highlighting the advantage of even or odd states.

Findings

Standard quantum limit can be beaten with even or odd states.

Optimal states can approach the Heisenberg limit for squeezed thermal states.

Parity measurement enables super-precision in phase estimation.

Abstract

We derive a general expression of the quantum Fisher information for a Mach-Zehnder interferometer, with the port inputs of an \emph{arbitrary} pure state and a squeezed thermal state. We find that the standard quantum limit can be beaten, when even or odd states are applied to the pure-state port. In particular, when the squeezed thermal state becomes a thermal state, all the even or odd states have the same quantum Fisher information for given photon numbers. For a squeezed thermal state, optimal even or odd states are needed to approach the Heisenberg limit. As examples, we consider several common even or odd states: Fock states, even or odd coherent states, squeezed vacuum states, and single-photon-subtracted squeezed vacuum states. We also demonstrate that super-precision can be realized by implementing the parity measurement for these states.