Search for: All records

Abstract Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states. 

Single-photon detectors (SPDs) are ubiquitous in many protocols for quantum imaging, sensing, and communications. Many of these protocols critically depend on the precise knowledge of their detection efficiency. A method for the calibration of SPDs based on sources of quantum-correlated photon pairs uses single-photon detection to generate heralded single photons, which can be used as a standard of radiation at the single-photon level. These heralded photons then allow for precise calibration of SPDs in absolute terms. In this work, we investigate the absolute calibration of avalanche photodiodes based on a portable, commercial bi-photon source, and investigate the effects of multi-photon events from the spontaneous parametric down conversion (SPDC) process in these sources. We show that the multi-photon character of the bi-photon source, together with system losses, has a significant impact on the achievable accuracy for the calibration of SPDs. However, modeling the expected photon counting statistics from the squeezed vacuum in the SPDC process allows for accurate estimation of the efficiency of SPDs, assuming that the system losses are known. This study provides essential information for the design and optimization of portable bi-photon sources for their application in on-site calibration of SPDs with high accuracy, without requiring any other reference standard. 

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0,\pi /2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0,\pi )$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology. 

Abstract Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understanding about their fundamental characteristics and demonstrate their superior performance, we develop a comprehensive statistical analysis based on Bayesian optimal design of experiments, which provides a natural description of these non-Gaussian strategies. This mathematical framework, together with numerical analysis and Monte Carlo methods, allows us to determine the asymptotic limits in sensitivity of strategies based on photon counting designed to maximize information gain, which up to now had been a challenging problem. Moreover, we show that these non-Gaussian phase estimation strategies have the same functional form as the canonical phase measurement in the asymptotic limit differing only by a scaling factor, thus providing the highest sensitivity among physically-realizable measurements for single-shot phase estimation of coherent states known to date. This work shines light into the potential of optimized non-Gaussian measurements based on photon counting for optical quantum metrology and phase estimation.