The importance of integrated quantum photonics in the telecom band is based on the possibility of interfacing with the optical network infrastructure that was developed for classical communications. In this framework, femtosecond laser-written integrated photonic circuits, which have already been assessed for use in quantum information experiments in the 800-nm wavelength range, have great potential. In fact, these circuits, being written in glass, can be perfectly mode-matched at telecom wavelength to the in/out coupling fibers, which is a key requirement for a low-loss processing node in future quantum optical networks. In addition, for several applications, quantum photonic devices must be dynamically reconfigurable. Here, we experimentally demonstrate the high performance of femtosecond laser-written photonic circuits for use in quantum experiments in the telecom band, and we demonstrate the use of thermal shifters, which were also fabricated using the same femtosecond laser, to accurately tune such circuits. State-of-the-art manipulation of single-and two-photon states is demonstrated, with fringe visibilities greater than 95%. The results of this work open the way to the realization of reconfigurable quantum photonic circuits based on this technological platform.

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...

Photon entanglement is an important state of light that is at the basis of many protocols in photonic quantum technologies, from quantum computing, to simulation and sensing. The capability to generate entangled photons in integrated waveguide sources is particularly advantageous due to the enhanced stability and more efficient light-crystal interaction. Here we realize an integrated optical source of entangled degenerate photons at telecom wavelength, based on the hybrid interfacing of photonic circuits in different materials, all inscribed by femtosecond laser pulses. We show that our source, based on spontaneous parametric down-conversion, gives access to different classes of output states, allowing to switch from path-entangled to polarization-entangled states with net visibilities above 0.92 for all selected combinations of integrated devices. * These authors contributed equally. †

Wave-particle duality is the most fundamental description of the nature of a quantum object, which behaves like a classical particle or wave depending on the measurement apparatus. On the other hand, entanglement represents nonclassical correlations of composite quantum systems, being also a key resource in quantum information. Despite the very recent observations of wave-particle superposition and entanglement, whether these two fundamental traits of quantum mechanics can emerge simultaneously remains an open issue. Here we introduce and experimentally realize a scheme that deterministically generates entanglement between the wave and particle states of two photons. The elementary tool allowing this achievement is a scalable single-photon setup which can be in principle extended to generate multiphoton wave-particle entanglement. Our study reveals that photons can be entangled in their dual wave-particle behavior and opens the way to potential applications in quantum information protocols exploiting the wave-particle degrees of freedom to encode qubits.

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.