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OSA Quantum 2.0 Conference

Experimental Demonstration of Multi-Parameter Estimation at the Ultimate Quantum Limit

Benjamin Brecht, Vahid Ansari, Jano Gil-López, John M. Donohue, Jaroslav Řeháček, Z. Hradil, Luis Lorenzo Sánchez-Soto, Christine Silberhorn

Published Jan 1, 2020• 2 citations
Publisher

Abstract

We demonstrate the quantum-limited simultaneous estimation of the timing centroid, offset, and intensity imbalance of an incoherent mixture of two single-photon level pulses. Our measurement saturates the quantum Cramér-Rao lower bound.
DOI
10.1364/quantum.2020.qw6a.17

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Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.
Photonic quantum metrology has demonstrated advantages in precision and resource efficiency for a wide range of applications, with several schemes approaching the fundamental quantum Cramér-Rao precision bound (QCRB). However, the intrinsic incompatibility of quantum measurements represents a hurdle in extending these advantages to the simultaneous estimation of multiple parameters. In this paper, we present an experimental protocol approaching the QCRB simultaneously in two polarisation parameters, across a wide range of the parameter space, with as few as ∼200\sim 200∼200 photon pairs, offering advantages for polarimetric sensing for dim sources such as in X-ray astronomy or photosensitive samples.