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arXiv:1507.07814

Quantum-enhanced multiparameter estimation in multiarm interferometers

Mario Arnolfo Ciampini, Nicolò Spagnolo, Chiara Vitelli, Luca Pezzè, Augusto Smerzi, Fabio Sciarrino

Published Jul 28, 2015• 3 citations
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Abstract

Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation beyond what reachable within classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful entanglement (among multimode particles, qudits) for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.

DOI
10.48550/arxiv.1507.07814

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In this work, we investigate the problem of multiphase estimation using generalized 333- and 444-mode Mach-Zehnder interferometer. In our setup, we assume that the number of unknown phases is the same as the number of modes in the interferometer, which introduces strong correlations between estimators of the phases. We show that despite these correlations and despite the lack of optimisation of a measurement strategy (a fixed interferometer is used) we can still obtain the Heisenberg-like scaling of precision of estimation of all the parameters. Our estimation scheme can be applied to the task of quantum-enhanced sensing in 3-dimensional interferometric configurations.
Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum resources. We propose an experimentally feasible scheme to reach Heisenberg-scaling precision in the simultaneous estimation of two unknown phase parameters in a Mach-Zehnder interferometer by using squeezed and coherent states of light as input and homodyne detections at the outputs. Our results open a new research paradigm in harnessing the full quantum advantage of multiparameter estimation in distributed quantum sensing and quantum information processing, as enabled by multiphoton quantum interference with scalable experimental resources.
We identify precision limits for the simultaneous estimation of multiple parameters in multimode interferometers. Quantum strategies to enhance the multiparameter sensitivity are based on entanglement among particles, modes, or combining both. The maximum attainable sensitivity of particle-separable states defines the multiparameter shot-noise limit, which can be surpassed without mode entanglement. Further enhancements up to the multiparameter Heisenberg limit are possible by adding mode entanglement. Optimal strategies that saturate the precision bounds are provided.
A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.