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1. Determination of the asymptotic limits of adaptive photon counting measurements for coherent-state optical phase estimation

   https://doi.org/10.1038/s41534-022-00601-8  

   Rodríguez-García, M. A.; DiMario, M. T.; Barberis-Blostein, P.; Becerra, F. E. (December 2022, npj Quantum Information)

   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. 

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2. Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit

   https://doi.org/10.22331/q-2024-09-25-1480  

   Rodríguez-García, M A; Becerra, F E (September 2024, Quantum)

   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. 

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3. Precision Bounds on Continuous-Variable State Tomography Using Classical Shadows

   https://doi.org/10.1103/PRXQuantum.5.010346  

   Gandhari, Srilekha; Albert, Victor V.; Gerrits, Thomas; Taylor, Jacob M.; Gullans, Michael J. (March 2024, PRX Quantum 5)

   Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called “classical shadows,” with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon-number-resolving, and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with high probability, we show that homodyne detection requires order O(N4+1/3) measurements in the worst case, whereas photon-number-resolving and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental analyses of homodyne tomography match closely with our theoretical predictions. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements. 

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4. Optimized communication strategies with binary coherent states over phase noise channels

   https://doi.org/10.1038/s41534-019-0177-4  

   DiMario, M. T.; Kunz, L.; Banaszek, K.; Becerra, F. E. (July 2019, npj Quantum Information)

   Abstract The achievable rate of information transfer in optical communications is determined by the physical properties of the communication channel, such as the intrinsic channel noise. Bosonic phase noise channels, a class of non-Gaussian channels, have emerged as a relevant noise model in quantum information and optical communication. However, while the fundamental limits for communication over Gaussian channels have been extensively studied, the properties of communication over Bosonic phase noise channels are not well understood. Here we propose and demonstrate experimentally the concept of optimized communication strategies for communication over phase noise channels to enhance information transfer beyond what is possible with conventional methods of modulation and detection. Two key ingredients are generalized constellations of coherent states that interpolate between standard on-off keying and binary phase-shift keying formats, and non-Gaussian measurements based on photon number resolving detection of the coherently displaced signal. For a given power constraint and channel noise strength, these novel strategies rely on joint optimization of the input alphabet and the measurement to provide enhanced communication capability over a non-Gaussian channel characterized in terms of the error rate as well as mutual information. 

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5. Measurement of a superconducting qubit with a microwave photon counter

   https://doi.org/10.1126/science.aat4625  

   Opremcak, A.; Pechenezhskiy, I. V.; Howington, C.; Christensen, B. G.; Beck, M. A.; Leonard, E.; Suttle, J.; Wilen, C.; Nesterov, K. N.; Ribeill, G. J.; et al (September 2018, Science)

   Fast, high-fidelity measurement is a key ingredient for quantum error correction. Conventional approaches to the measurement of superconducting qubits, involving linear amplification of a microwave probe tone followed by heterodyne detection at room temperature, do not scale well to large system sizes. We introduce an approach to measurement based on a microwave photon counter demonstrating raw single-shot measurement fidelity of 92%. Moreover, the intrinsic damping of the photon counter is used to extract the energy released by the measurement process, allowing repeated high-fidelity quantum nondemolition measurements. Our scheme provides access to the classical outcome of projective quantum measurement at the millikelvin stage and could form the basis for a scalable quantum-to-classical interface. 

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