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1. Demonstration of optimal non-projective measurement of binary coherent states with photon counting

   https://doi.org/10.1038/s41534-022-00595-3  

   DiMario, M. T.; Becerra, F. E. (July 2022, npj Quantum Information)

   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. 

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2. Review—Electronic Circuit Systems for Piezoelectric Resonance Sensors

   https://doi.org/10.1149/1945-7111/ab6cf7  

   Park, Jong-Yoon; Choi, Jin-Woo (February 2020, Journal of The Electrochemical Society)

   Piezoelectric mass sensors have been widely studied for a variety of applications as a biological or chemical sensing transducer. With an increasing range of application areas and performance requirements for fast measurement time, higher resolution and accuracy, and compact system size, different measurement electronic systems have also been investigated to fulfill the performance requirements. Selecting a proper type of measurement electronics is critical to develop an optimized sensing system for practical applications. In this review, we cover different types of measurement electronics configurations including impedance-based measurement, oscillator-based measurement, and ring-down technique. Also, we provide an overview of the recent advances of each measurement electronics configuration for piezoelectric resonator sensors. Finally, the pros and cons of each measurement electronic configuration are compared and discussed. 

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3. Cosine Error Elimination Method for One-Dimensional Convex and Concave Surface Profile Measurements

   https://doi.org/10.1115/1.4046078  

   Guo, Xiangyu; Han, Jaemin; Lee, ChaBum (April 2020, Journal of Manufacturing Science and Engineering)

   Abstract This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed. 

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4. Cosine Error Elimination Method for One-Dimensional Convex and Concave Surface Profile Measurements

   https://doi.org/10.1115  

   Xiangyu Guo, Jaemin Han (February 2020, Journal of manufacturing science and engineering)

   This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed. 

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5. Pretty good measurement for bosonic Gaussian ensembles

   Mishra, Hemant K; Lami, Ludovico; Mandayam, Prabha; Wilde, Mark M (May 2024, International journal of quantum information)

   The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories. 

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