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Quantum Information and Measurement (QIM)

Adaptive two-phase estimation on a photonic integrated device

Mauro Valeri, Emanuele Polino, Davide Poderini, Nicolò Spagnolo, Fabio Sciarrino, Ilaria Gianani, Giacomo Corrielli, Andrea Crespi, Roberto Osellame

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Efficient adaptive multiphase estimation has been demonstrated experimentally on an integrated three-arm interferometer injected by single photons. Bayesian learning and Sequential Monte Carlo approximation have been employed as machine learning tools to achieve this goal.
DOI
10.1364/qim.2021.tu2a.5

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Summary form only given. Phase estimation represents one of the most notable examples in the context of the quantum metrology. The aim is to improve the capabilities to measure an unknown phase shift between the arms of an interferometer with respect to classical strategies by adopting quantum resources. Applications of the phase estimation task can be found in different contexts, such as imaging, measurements on biological systems, or gravitational wave detection [1]. While the theoretical and experimental frameworks for the single parameter case are well established, several open questions arise when extending the scenario to multiparameter estimation. Indeed, when the number of parameters to be estimated is larger than one, it is not trivial to saturate the ultimate bounds for all parameters simultaneously [2]. Hence, it becomes crucial to identify and implement experimentally a suitable platform to develop appropriate protocols for efficient multiphase estimation protocols. Here, we report [3] the experimental implementation of an interferometric platform to investigate experimentally multiphase estimation protocols. Such platform, shown in Fig. 1, is implemented by adopting the femtosecond laser micromachining technology, that allows to realize integrated photonic circuits including several optical elements. The implemented interferometer (Fig. 1) is composed of a first unitary transformation for state preparation, namely a balanced tritter [4,5], a second stage for internal phases, and a second unitary transformation for measurement of the output state. Reconfigurability in the device is inserted by means of thermo-optic phase shifters, that allow to tune the optical phases by applying a voltage on gold-plated resistors placed on top of the waveguides [6]. Resistors pattern on the device has been realized by using the same laser writing technology employed to implement the interferometric structure. We have then performed a multiphase estimation experiment by injecting two-photon input states within the interferometer for simultaneous measurement of two phases.
Multiparameter estimation is a general problem that aims at measuring unknown physical quantities, obtaining high precision in the process. In this context, the adoption of quantum resources promises a substantial boost in the achievable performances with respect to the classical case. However, several open problems remain to be addressed in the multiparameter scenario. A crucial requirement is the identification of suitable platforms to develop and experimentally test novel efficient methodologies that can be employed in this general framework. We report the experimental implementation of a reconfigurable integrated multimode interferometer designed for the simultaneous estimation of two optical phases. We verify the high-fidelity operation of the implemented device, and demonstrate quantum-enhanced performances in two-phase estimation with respect to the best classical case, post-selected to the number of detected coincidences. This device can be employed to test general adaptive multiphase protocols due to its high reconfigurability level, and represents a powerful platform to investigate the multiparameter estimation scenario.
Abstract Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources.
Phase estimation has applications from quantum imaging to gravitational-wave detection. In areas such as biological-system sampling or quantum metrology, it is crucial to optimally acquire information from a very limited number of probes. To address this need, the authors describe and experimentally verify a machine-learning method for optimal adaptive single-photon phase estimation based on a small number of trials. This approach could be used to optimize quantum metrology protocols, and can be extended to general multiparameter scenarios.