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Physical Review A

Modulation-agnostic single-shot estimation of quantum measurement confidence

M. V. Jabir, N. Fajar R. Annafianto, Abdella Battou, Ivan A. Burenkov, Sergey V. Polyakov

Published Nov 2, 2023• 1 citation
Publisher

Abstract

We experimentally explore single-shot state identification using long alphabets of states and employing different modulation schemes. We use time-resolved quantum measurement and Bayesian inference to identify the input state and demonstrate the advantage of this single-shot measurement over classical state identification. For each single-shot measurement, we estimate the confidence of state identification based on the quantum measurement and demonstrate the physical significance of confidence estimates. Particularly, we show that a set of confidence values correctly represents the probabilities of successful state identification for a given experimental outcome. We investigate the alphabets of coherent states with different modulations and show that confidence estimates yield the reliability of each act of measurement independently of the modulation used.

DOI
10.1103/physreva.108.052203

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We experimentally explore single-shot state identification using long alphabets of states and employing different modulation schemes. We use time-resolved quantum measurement and Bayesian inference to identify the input state and demonstrate the advantage of this single-shot measurement over classical state identification. For each single-shot measurement, we estimate the confidence of state identification based on the quantum measurement and demonstrate the physical significance of confidence estimates. Particularly, we show that a set of confidence values correctly represents the probabilities of successful state identification for a given experimental outcome. We investigate the alphabets of coherent states with different modulations and show that confidence estimates yield the reliability of each act of measurement independently of the modulation used.
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Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the phase of an electromagnetic field and single-shot measurements of this phase are necessary. While there are measurements able to estimate the phase of light in a single shot with small uncertainties, demonstrations of near-optimal single-shot measurements for an unknown phase of a coherent state remain elusive. Here, we propose and demonstrate strategies for single-shot measurements for ab initio phase estimation of coherent states that surpass the sensitivity limit of heterodyne measurement and approach the Cramer-Rao lower bound for coherent states. These single-shot estimation strategies are based on real-time optimization of coherent displacement operations, single photon counting with photon number resolution, and fast feedback. We show that our demonstration of these optimized estimation strategies surpasses the heterodyne limit for a wide range of optical powers without correcting for detection efficiency with a moderate number of adaptive measurement steps. This is, to our knowledge, the most sensitive single-shot measurement of an unknown phase encoded in optical coherent states.
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