Multiparameter transmission estimation at the quantum Cram\'er-Rao limit on a cloud quantum computer

TL;DR

This paper demonstrates quantum multiparameter transmission estimation at the quantum Cramér-Rao limit using a cloud-based quantum photonic device, achieving high-precision parameter estimates through maximum likelihood estimation.

Contribution

It introduces a protocol for simultaneous loss parameter estimation in a quantum optical system on a cloud quantum computer, approaching fundamental quantum limits.

Findings

Achieved transmission estimates with uncertainties near the quantum Cramér-Rao bound.

Successfully performed maximum likelihood estimation on over a million photon detection events.

Provided insights into quantum multiparameter estimation and device characterization.

Abstract

Estimating transmission or loss is at the heart of spectroscopy. To achieve the ultimate quantum resolution limit, one must use probe states with definite photon number and detectors capable of distinguishing the number of photons impinging thereon. In practice, one can outperform classical limits using two-mode squeezed light, which can be used to herald definite-photon-number probes, but the heralding is not guaranteed to produce the desired probes when there is loss in the heralding arm or its detector is imperfect. We show that this paradigm can be used to simultaneously measure distinct loss parameters in both modes of the squeezed light, with attainable quantum advantages. We demonstrate this protocol on Xanadu's X8 chip, accessed via the cloud, building photon-number probability distributions from $10^6$ shots and performing maximum likelihood estimation (MLE) on these distributions $10^3$ independent times. Because pump light may be lost before the squeezing occurs, we also simultaneously estimate the actual input power, using the theory of nuisance parameters. MLE converges to estimate the transmission amplitudes in X8's eight modes to be 0.39202(6), 0.30706(8), 0.36937(6), 0.28730(9), 0.38206(6), 0.30441(8), 0.37229(6), and 0.28621(8) and the squeezing parameters, which are proxies for effective input coherent-state amplitudes, their losses, and their nonlinear interaction times, to be 1.3000(2), 1.3238(3), 1.2666(2), and 1.3425(3); all of these uncertainties are within a factor of two of the quantum Cram\'er-Rao bound. This study provides crucial insight into the intersection of quantum multiparameter estimation theory, MLE convergence, and the characterization and performance of real quantum devices.