Quantum metrology for non-linear phase shifts with entangled coherent states

TL;DR

This paper explores how entangled coherent states can enhance phase estimation in non-linear quantum metrology, demonstrating their superiority over NOON states and analyzing practical generation methods and loss effects.

Contribution

It introduces optimized phase estimation using entangled coherent states in non-linear settings and proposes feasible creation methods with current optical technology.

Findings

Entangled coherent states outperform NOON states in non-linear phase estimation.

Approximate ECSs can be generated from squeezed vacuum with slight advantages.

Loss effects in non-linear interferometers are analyzed for practical scenarios.

Abstract

We investigate the phase enhancement of quantum states subject to non-linear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states and of odd ECS states with the same average particle number <n> and non-linearity exponent k. We investigate the creation of approximate ECSs (AECSs) from a squeezed vacuum with current optical technology methods and find that a pure AECS is even slightly better than an even ECS for large <n>. We also examine simple but physically relevant cases of loss in the non-linear interferometer arm, for a fixed <n>.