Adaptive protocols for SU(11) interferometers to achieve ab initio phase estimation at the Heisenberg limit

TL;DR

This paper proposes adaptive protocols for SU(11) interferometers to achieve optimal phase estimation at the Heisenberg limit, extending applicability to larger phase shifts through feedback tuning and optimal measurement strategies.

Contribution

It introduces two adaptive protocols for SU(11) interferometers that improve phase estimation beyond small phase shifts, utilizing feedback tuning and optimal measurement without fine tuning.

Findings

Achieves Heisenberg limit for larger phase shifts

Demonstrates effectiveness of adaptive feedback protocols

Proposes implementation strategies for optimal measurements

Abstract

The precision of phase estimation with interferometers can be greatly enhanced using non-classical quantum states, and the SU(11) interferometer is an elegant scheme, which generates two-mode squeezed state internally and also amplifies the signal. It has been shown in [Phys. Rev. A {\bf 95}, 063843 (2017)] that the photon-number measurement can achieve the Heisenberg limit, but only for estimating a small phase shift. We relax the constraint on the phase size by considering two adaptive protocols: one also uses the photon-number measurement with a specially tuned sequence of feedback phase; the other implements the yet-to-be-realised optimal measurement but without fine tuning.