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Scientific Reports

Quantum-enhanced multiparameter estimation in multiarm interferometers

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

Published Jul 6, 2016• 104 citations
Publisher

Abstract

Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by 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 particle (qudit) entanglement for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We theoretically 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
10.1038/srep28881

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Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by 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 particle (qudit) entanglement for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We theoretically 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.
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.
Quantum-enhanced interferometers have been widely used in single-parameter precision measurement, and multiparameter precision measurement is the building block of numerous sensing and imaging applications. However, it remains challenging to realize high-sensitivity multiparameter sensing without increasing power, which is crucial for biological science. Here, we propose and demonstrate a deterministic quantum-enhanced interferometer, where high-sensitivity multiparameter sensing is realized by effectively squeezing noises and amplifying signals. Key technologies are essential to the results, including the parallel and sequential use of squeezed states inside the interferometer. Notably, in the quantum-enhanced three-arm interferometer, not only joint but also individual values of three signals are simultaneously measured with a signal-to-noise ratio of more than 10.37±0.13 dB compared with that of the conventional interferometer under the same phase-sensing power. These advances constitute a critical step toward observing multiple elusive signals and give rise to a wide range of sensing and imaging applications.
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.
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.
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.
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.