Quantum metrology is one of the most promising applications of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here, the authors review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to phase estimation. The authors describe the current state of the art in the field in terms of platforms and quantum resources. Furthermore, the authors present the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time. The authors conclude by discussing the current experimental and theoretical challenges and the open questions toward implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise.

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.

Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical parameters with improved precision over classical strategies. Within this context, most theoretical and experimental studies have focused on determining the fundamental bounds and how to achieve them in the asymptotic regime where a large number of resources is employed. However, in most applications it is necessary to achieve optimal precisions by performing only a limited number of measurements. To this end, machine learning techniques can be applied as a powerful optimization tool. Here, we implement experimentally single-photon adaptive phase estimation protocols enhanced by machine learning, showing the capability of reaching optimal precision after a small number of trials. In particular, we introduce a new approach for Bayesian estimation that exhibit best performances for very low number of photons N . Furthermore, we study the resilience to noise of the tested methods, showing that the optimized Bayesian approach is very robust in the presence of imperfections. Application of this methodology can be envisaged in the more general multiparameter case, that represents a paradigmatic scenario for several tasks including imaging or Hamiltonian learning.Introduction. -Quantum metrology is one of the most promising applications of quantum theory [1][2][3][4][5], where the aim is to obtain enhanced performances in the estimation of unknown physical parameters by employing quantum resources. A notable benchmark for quantum metrology is provided by phase estimation, a task where the parameter to be measured is an optical phase embedded within an interferometric setup. In this scenario, an input probe field is prepared in a suitable state and sent through the system. The value of the phase is retrieved by measuring the field after the evolution in the interferometer, and by repeating the procedure N times to perform statistical analysis. While the ultimate precision achievable with classical resources is known to be bounded by the standard quantum limit (SQL), stating that the achievable error on the unknown phase φ scales as N −1/2 (being N the number of photons), the adoption of quantum inputs can in principle improve the performances up to the Heisenberg limit (HL) [1,2], scaling as N −1 . Several theoretical and experimental studies [6][7][8][9][10][11][12][13][14] focused on devising experimental schemes able to reach quantum enhanced performances. Furthermore, recent advances in integrated photonics has opened new possibilities for the implementation and the development of phase estimation protocols [15][16][17][18][19][20][21][22]. In parallel, a thorough investigation has been dedicated to identifying the effect of experimental noise and losses [23][24][25][26]. In the scenario where the parameter to be estimated is a single phase, it is always possible to identify the op...

The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. Onedimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states.Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in photonics platforms, paving the way for the use of such a quantum state-engineering toolbox for a large range of applications.

Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the non-trivial correlations between optical polarization and orbital angular momentum. Here we demonstrate a new, flexible experimental approach to the classification of vortex vector beams. We first describe a platform for generating arbitrary complex vector vortex beams inspired to photonic quantum walks. We then exploit recent machine learning methods -namely convolutional neural networks and principal component analysis -to recognize and classify specific polarization patterns. Our study demonstrates the significant advantages resulting from the use of machine learning-based protocols for the construction and characterization of high-dimensional resources for quantum protocols.Introduction-Light is endowed with Orbital Angular Momentum (OAM) [1, 2], a degree of freedom associated with structured, non-plane wavefronts, and characterized by an azimuthal phase dependence. When a nontrivial phase dependence is coupled with a helicoidal transverse polarization pattern, one talks of a Vector Vortex Beam (VVB) [2,3]. The interest in such states is motivated by the applications in multiple fields of classical and quantum optics [4,5]: from particle trapping to metrological applications in microscopy [6,7], and for OAM-based communications schemes in free-space and in-fibre [8,9]. VVBs are also often employed in quantum information protocols due to the hyperentanglement between their polarization and spatial degrees of freedom. Photonic platforms for quantum sensing and metrology leveraging such encoding have also been reported [10,11]. OAM-based schemes for investigating quantum causal structures [12], quantum communication and cryptography [13][14][15][16][17][18], quantum walks [19][20][21], quantum simulation [22,23], and quantum state engineering [24,25], have been previously demonstrated.Despite the potential of VVBs, many questions regarding the decoding of information stored in OAM and polarization remain unanswered. Various techniques of OAMdemultiplexing envisage the need of additional instruments -such as interferometry [26][27][28] or spatial filtering [29][30][31] -to be efficiently implemented. These introduce detrimental effects of loss and noise [32]. Moreover, the challenge of performing state tomography in such a high-dimensional framework, a fundamental task in quantum information processing [33,34], can hardly be overestimated. The design and demonstration of reliable techniques for the generation and classification of VVBs is thus highly desirable. Indeed, substantive efforts on finding novel platforms are subject of intense research activities [6,7,35,36], including in integrated photonics [37][38][39] and generation by plasmonic metasurfaces [40,41].Recently, Machine Learning (ML) has emerged as a versatile toolbox to tackle a variety of tasks arising in experi-