A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry

TL;DR

This paper investigates the fundamental trade-offs in quantum interferometry when estimating both phase and loss simultaneously, revealing that optimal precision for both cannot be achieved at once and proposing optimal quantum states for best possible joint estimation.

Contribution

It derives a fundamental trade-off in simultaneous quantum-limited estimation of phase and loss, and designs optimal quantum states for this task.

Findings

A fundamental trade-off limits simultaneous phase and loss estimation.

Optimal quantum states are identified for best joint estimation.

Implications for quantum sensing and imaging scenarios.

Abstract

Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not attainable, leading to trade-offs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a trade-off in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strategy saturating the quantum Cramer-Rao bound for loss and phase estimation in a single setup simultaneously. We design optimal quantum states with a fixed number of photons achieving the best possible simultaneous precisions. Our results reveal general features about concurrently estimating Hamiltonian and dissipative parameters, and has implications for sophisticated sensing scenarios such as quantum imaging.