Optimal gain sensing of quantum-limited phase-insensitive amplifiers

TL;DR

This paper establishes the quantum limit for gain estimation in phase-insensitive optical amplifiers using entangled multimode probes, demonstrating quantum advantages over classical methods and deriving key theoretical bounds.

Contribution

It introduces the quantum limit for gain sensing with multimode entangled probes and compares quantum and classical strategies, providing new theoretical insights.

Findings

Quantum limit on gain estimation precision established.

Entangled multimode probes outperform classical probes.

Quantum advantage persists even with imperfect detection.

Abstract

Phase-insensitive optical amplifiers uniformly amplify each quadrature of an input field and are of both fundamental and technological importance. We find the quantum limit on the precision of estimating the gain of a quantum-limited phase-insensitive optical amplifier using a multimode probe that may also be entangled with an ancilla system. In stark contrast to the sensing of loss parameters, the average photon number $N$ and number of input modes $M$ of the probe are found to be equivalent and interchangeable resources for optimal gain sensing. All pure-state probes whose reduced state on the input modes to the amplifier is diagonal in the multimode number basis are proven to be quantum-optimal under the same gain-independent measurement. We compare the best precision achievable using classical probes to the performance of an explicit photon-counting-based estimator on quantum probes and show that an advantage exists even for single-photon probes and inefficient photodetection. A closed-form expression for the energy-constrained Bures distance between two product amplifier channels is also derived.