Quantum metrology represents one of the most promising applications of quantum theory. In this context, quantum resources are employed to improve the sensitivity in the estimation of one or more unknown physical parameters. The adoption of quantum probe state promises to disclose the capability of reaching the fundamental Heisenberg limit, thus achieving better performances than any classical strategy. While the theoretical framework in the single-parameter scenario is well established and several schemes have been tested experimentally, the multiparameter case still presents several open problems. These include for instance the identification of the ultimate bounds, as well as the capability of performing optimal measurements in the general scenario.
A crucial requirement is then to identify a suitable testbench to investigate and develop suitable methodologies for multiparameter estimation. This platform is provided by multiarm interferometers, where the parameters to be measured are a set of unknown optical phases. Recent development in quantum integrated photonics have opened new possibilities in this direction, including the capability of fabricating reconfigurable phase shifters in complex networks.
The aim of this project is to perform first multiphase estimation experiments in an integrated photonic platform. By adopting multiphoton input states, we will pursue the capability of reaching quantum-enhanced performances in this task. Throughout the project we will also study and develop suitable adaptive protocols for this scenario, and apply such protocols in the implemented platform. The obtained results will provide a first step towards developing general recipes for quantum-enhanced multiparameter estimation, with several applications such as imaging, gravitational wave detection, or measurement in biological systems. Indeed, integrated multiarm interferometers represent a promising platform to be employed as a paradigmatic system for this scenario.
The aim of this project is to report first multiphase estimation experiments in an integrated platform, and to reach quantum-enhanced performances in the estimation process. This platform presents several advantages, such as tunability and stability, where the adoption of thermo-optic phase shifters will allow to perform adaptive protocols. Bu using this approach the control parameters, the input and output transformations can be tuned throughout the process to optimize the extraction of information. In the multiparameter scenario, only a few experimental results have been reported, all of them dealing with the simultaneous estimation of an optical phase and a noise term such as dissipation or phase diffusion. These implementations include for instance the joint estimation of phase and phase diffusion [20], phase and quality of the probe state [21], or the discrimination of an actual signal from parasitic interference [31]. However, no experimental results have been reported yet on quantum-enhanced simultaneous estimation of multiple phases.
The expected outcome of this project will then provide first results in this direction, by showing the possibility of reaching quantum-enhanced performances in multiphase estimation for an actual scenario. These results will provide first insights on the potentiality of integrated photonics for this purpose. The capability of reaching quantum-enhanced performances is particularly relevant in the multiparameter case [5], since a large variety of estimation problems involve more than a single physical quantity. This is for instance the case of phase imaging [32-34], measurements on biological systems [9,35], magnetic field imaging [36], gravitational waves parameters estimation [6,37], sensing technologies [38], or quantum sensing networks [25]. The relevance of the applications of quantum metrology has been confirmed within the European flasghip on quantum technologies, since such task has been identified as one of the four main pillars. Quantum sensing thus represents one of the most promising applications of quantum theory.
The integrated platform adopted in this project can provide a significant benchmark system to investigate and develop novel approaches for multiparameter estimation in more complex networks. Indeed, recent advances in integrated quantum photonics [39] have shown that it is possible to fabricate structures with a large number of modes, including several reconfigurable elements.
Besides being a benchmark platform, those methods for multiparameter estimation can be a significant tool for quantum technology characterization. Indeed, while fabrication capabilities have enabled the possibility of building complex quantum devices, it is nevertheless crucial to identify appropriate methods to test and characterize their dynamical operating regime. This becomes particularly relevant when scaling up the system size, whose evolution is governed by a progressively larger number of parameters. Hence, the possibility of applying efficient methods able to reach high sensitivity with a limited number of resources can boost the capability of identifying patologies in the fabrication process.
In general, the definition of general recipes to optimally extract information from an unknown system can be applied in the general case of quantum process tomography [40] and state estimation [41]. In those contexts, which deals with Hilbert spaces whose dimension increases fast with the system size, several methods have been developed in the last years. However, only recently attention has been dedicated to optimizing such process in terms of number of necessary resources.
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[38] P. A. Ivanov, et al., arXiv:1801.04764 (2018).
[39] N. C. Harris, et al., Nature Photon. 11, 447 (2017).
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[41] Y. Yang, et al., arXiv:1802.07587 (2018).