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Quantum Sensing is a rapidly growing branch of research within the area of quantum science and technology offering key resources, beyond classical ones, with potential for commercialisation of novel (quantum) sensors. The exploitation of quantum resources offered by photons can boost the performance of quantum sensors for innovative and challenging applications. In this paper we build on the idea of the Quantum Ghost Spectroscopy (QGS), i.e. the counterpart in the frequency domain of Quantum Ghost Imaging (QGI), targeting specific applications in the detection of possible threats. This is implemented by exploiting the opportunities offered by Quantum Optics, i.e. the generation of photon pairs characterized by spectral correlations. We will discuss our main results obtained with pure QGS experiments showing that it is possible to assess the presence of a target dealing with a low resources measurement. The time-frequency domain reveals a huge potential for several applications and frequency correlations represent a versatile tool that can be exploited to enable the spectral analysis of objects where a direct measurement would not be feasible (e.g. security). The use of nondegenerate sources of correlated photons allowed to reveal spectral features in the near infrared wavelengths employing the usual detectors for the visible region.

Reliably characterised pulses are the starting point of any application of ultrafast techniques. Unfortunately, experimental constraints do not always allow optimising the characterisation conditions. This dictates the need for refined analysis methods. Here we show that neutral networks can provide a viable characterisation when applied to data from SPIDER. We have adopted a cascade of convolutional networks, addressing the multiparameter structure of the interferogram with a reasonable computing power. In particular, the necessity of precalibration is reduced, thus pointing towards the introduction of neural networks in more generic arrangements.

We show how quantum coherence governs the quasiprobability statistics of outcome pairs, consecutively recorded at two distinct times, using weak measurements. In doing this, we have realised weak-sequential measurement with photonic qubits, where the first measurement is carried out by a positive operator-valued measure, whereas the second one is a projective operation. We determine the quasiprobability distributions associated to this procedure, based on both the commensurate and the Margenau-Hill approach, by establishing a link between these descriptions. Our results find application to quantum monitoring aimed at implementing or stabilising task without completely loosing the initial quantum coherence., Comment: 6 pages, 3 figures. Comments and feedback are welcome

Quantum steering captures the ability of one party, Alice, to control through quantum correlations the state at a distant location, Bob, with superior ability than allowed by a local hidden state model. Verifying the presence of quantum steering has implications for the certification of quantum channels, and its connection to the metrological power of the quantum state has been recently proved. This link is established by means of the violation of a Cram\'er-Rao bound holding for non-steerable states: its direct assessment would then require operation in the asymptotic regime of a large number of repetitions. Here, we extend previous work to account explicitly for the use of a limited number of resources, and put this modified approach to test in a quantum optics experiment. The imperfections in the apparatus demand an adaptation of the original test in the multiparameter setting. Our results provide guidelines to apply such a metrological approach to the validation of quantum channels.

Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement noise susceptibility now allows to quantify the robustness of measurement for single-parameter estimation. Here we extend this notion to the multiparameter quantum estimation scenario. We provide its mathematical definition in the form of a semidefinite program. Although a closed formula could not be found, we further derive an upper and a lower bound to the susceptibility. We then apply these techniques to two paradigmatic examples of multiparameter estimation: the joint estimation of phase and phase-diffusion and the estimation of the different parameters describing the incoherent mixture of optical point sources. Our figure of merit provides clear indications on conditions allowing or hampering robustness of multiparameter measurements.

The introduction of quantum methods in spectroscopy can provide enhanced performance and technical advantages in the management of noise. We investigate the application of quantum illumination in a pump and probe experiment. Thermal lensing in a suspension of gold nanorods is explored using a classical beam as the pump and the emission from parametric downconversion as the probe. We obtain an insightful description of the behaviour of the suspension under pumping with a method known to provide good noise rejection. Our findings are a further step towards investigating effects of quantum light in complex plasmonic media.

We present a device that exploits spatial and spectral correlations in parametric downconversion at once. By using a ghost imaging arrangement, we have been able to reconstruct remotely the frequency profile of a composite system. The presence of distinct spectral regions is corroborated by a model-independent statistical analysis that constitutes an intriguing possibility also in the low count regime.

In the past years, optical fluorescence microscopy (OFM) made steady progress towards increasing the localisation precision of fluorescent emitters in biological samples. The high precision achieved by these techniques has prompted new claims, whose rigorous validation is an outstanding problem. For this purpose, local estimation theory (LET) has emerged as the most used mathematical tool. We establish a novel multi-parameter estimation framework that captures the full complexity of single-emitter localisation in an OFM experiment. Our framework relies on the fact that there are other unknown parameters alongside the emitter's coordinates, such as the average number of photons emitted (brightness), that are correlated to the emitter position, and affect the localisation precision. The increasing complexity of a multi-parameter approach allows for a more accountable assessment of the precision. We showcase our method with MINFLUX microscopy, the OFM approach that nowadays generates images with the best resolution. Introducing the brightness as an unknown parameter, we shed light on features that remain obscure in the conventional approach: the precision can be increased only by increasing the brightness, (i.e., illumination power or exposition time), whereas decreasing the beam separation offers limited advantages. We demonstrate that the proposed framework is a solid and general method for the quantification of single-emitter localisation precision for any OFM approach on equal footing, evaluating the localization precision of stimulated emission depletion (STED) microscopy and making a comparison with MINFLUX microscopy., Comment: 20 pages, 4 figures

Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology., Comment: 8 pages, 6 figures

Assessing the presence of chemical, biological, radiological and nuclear threats is a crucial task which is usually dealt with by analyzing the presence of spectral features in a measured absorption profile. The use of quantum light allows to perform these measurements remotely without compromising the measurement accuracy through ghost spectrometry. However, in order to have sufficient signal-to-noise ratio, it is typically required to wait long acquisition times, hence subtracting to the benefits provided by remote sensing. In many instances, though, reconstructing the full spectral lineshape of an object is not needed and the interest lies in discriminating whether a spectrally absorbing object may be present or not. Here we show that this task can be performed fast and accurately through ghost spectrometry by comparing the low resources measurement with a reference. We discuss the experimental results obtained with different samples and complement them with simulations to explore the most common scenarios.

Control and characterization of networks is a paramount step for the development of many quantum technologies. Even for moderate-sized networks, this amounts to explore an extremely vast parameters space in search for the couplings defining the network topology. Here we explore the use of a genetic algorithm to retrieve the topology of a network from the measured probability distribution obtained from the evolution of a continuous-time quantum walk on the network. Our result shows that the algorithm is capable of efficiently retrieving the required information even in the presence of noise.

Recovering the original spectral lineshapes from data obtained by instruments with extended transmission profiles is a basic tenet in spectroscopy. By using the moments of the measured lines as basic variables, we turn the problem into a linear inversion. However, when only a finite number of these moments are relevant, the rest of them act as nuisance parameters. These can be taken into account with a semiparametric model, which allows us to establish the ultimate bounds on the precision attainable in the estimation of the moments of interest. We experimentally confirm these limits with a simple ghost spectroscopy demonstration.

Two-photon interference underlies the functioning of many quantum photonics devices. It also serves as the prominent tool for testing the indistinguishability of distinct photons. However, as their time-spectral profile becomes more involved, extracting relevant parameters, foremost the central frequency difference, may start suffering difficulties. In a parametric approach, these arise from the need for an exhaustive model combined with limited count statistics. Here we discuss a solution to curtail these effects on the evaluation of frequency separation relying on a semiparametric method. The time trace of the quantum interference pattern of two photons from two independent solid-state emitters is preprocessed by means of singular spectral analysis before inspecting its spectral content. This approach allows to single out the relevant oscillations from both the envelope and the noise, without resorting to fitting. This opens the way for robust and efficient on-line monitoring of quantum emitters.

Characterization of quantum objects, being them states, processes, or measurements, complemented by previous knowledge about them is a valuable approach, especially as it leads to routine procedures for real-life components. To this end, Machine Learning algorithms have demonstrated to successfully operate in presence of noise, especially for estimating specific physical parameters. Here we show that a neural network (NN) can improve the tomographic estimate of parameters by including a convolutional stage. We applied our technique to quantum process tomography for the characterization of several quantum channels. We demonstrate that a stable and reliable operation is achievable by training the network only with simulated data. The obtained results show the viability of this approach as an effective tool based on a completely new paradigm for the employment of NNs operating on classical data produced by quantum systems.

High-performing nanomaterials are paramount for advanced photonic technologies, like sensing, lasing, imaging, data storage, processing, and medical and biological applications. Metal nanoparticles play a key role, because the localized surface plasmonic resonances enhance the linear and nonlinear optical properties of hosting materials, thus increasing the range of applications. The improved optical response results in an enriched and largely unexplored phenomenology. In the present work, we show the formation and interaction of two dispersive shock waves emerging by illuminating an aqueous suspension of gold nanorods with a pulsed laser beam. By analyzing the characteristic undular bores that regularize a shock front in a dispersive material, we were able to distinguish dispersive shock waves of different origins, i.e., electronic and thermal, first coexisting and then interacting to form a double front of equal intensity. The observed scenario agrees with existing literature reporting an electronic and thermal contribution to the nonlinear refractive index of material containing gold nanoparticles. Although a full comprehension of the reported results deserves an analytical description, they already pave the way to using materials containing metal nanoparticles as a platform for studying fundamental extreme nonlinear phenomena and developing novel solutions for sensing and control.

The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, thus it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with $n$-neighbour interactions using a deep neural network model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.

Measurements in the quantum domain can exceed classical notions. This concerns fundamental questions about the nature of the measurement process itself, as well as applications, such as their function as building blocks of quantum information processing protocols. In this paper we explore the notion of entanglement for detection devices in theory and experiment. A method is devised that allows one to determine nonlocal quantum coherence of positive-operator-valued measures via negative contributions in a joint distribution that fully describes the measurement apparatus under study. This approach is then applied to experimental data for detectors that ideally project onto Bell states. In particular, we describe the reconstruction of the aforementioned entanglement quasidistributions from raw data and compare the resulting negativities with those expected from theory. Therefore, our method provides a versatile toolbox for analyzing measurements regarding their quantum-correlation features for quantum science and quantum technology., Comment: version accepted for publication

Quantum coherence is a central ingredient in quantum physics with several theoretical and technological ramifications. In this work we consider a figure of merit encoding the information on how the coherence generated on average by a quantum gate is affected by unitary errors (coherent noise sources). We provide numerical evidences that such information is well captured by the statistics of local energy measurements on the output states of the gate. These findings are then corroborated by experimental data taken in a quantum optics setting.

We apply the theory of semiparametric estimation to a Hong-Ou-Mandel interference experiment with a spectrally entangled two-photon state generated by spontaneous parametric downconversion. Thanks to the semiparametric approach we can evaluate the Cram\'er-Rao bound and find an optimal estimator for a particular parameter of interest without assuming perfect knowledge of the two-photon wave function, formally treated as an infinity of nuisance parameters. In particular, we focus on the estimation of the Hermite-Gauss components of the marginal symmetrised wavefunction, whose Fourier transform governs the shape of the temporal coincidence profile. We show that negativity of these components is an entanglement witness of the two-photon state.

Capturing specific kinds of quantum correlation is of paramount importance for quantum networking. Different routes can be taken to achieve this task, highlighting different novel aspects of such quantum correlations. Following the recent theoretical results by Yadin, Fadel and Gessner [Nat. Commun. 12, 2410 (2021)], we demonstrate experimentally how steering manifests in the metrological abilities of a bipartite state. Our results confirm the relevance of this novel approach, and compare the outcome with already employed alternatives., Comment: New version including the material in the Erratum

The ultimate precision in any measurement is dictated by the physical process implementing the observation. The methods of quantum metrology have now succeeded in establishing bounds on the achievable precision for phase measurements over noisy channels. In particular, they demonstrate how the Heisenberg scaling of the precision can not be attained in these conditions. Here we discuss how the ultimate bound in presence of loss has a physical motivation in the Kramers-Kronig relations and we show how they link the precision on the phase estimation to that on the loss parameter.

The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the proposal to embed classical data into quantum ones: these live in the more complex Hilbert space where they can get split into linearly separable clusters. Here, we implement these ideas by engineering two different experimental platforms, based on quantum optics and ultra-cold atoms respectively, where we adapt and numerically optimize the quantum embedding protocol by deep learning methods, and test it for some trial classical data. We perform also a similar analysis on the Rigetti superconducting quantum computer. Therefore, we find that the quantum embedding approach successfully works also at the experimental level and, in particular, we show how different platforms could work in a complementary fashion to achieve this task. These studies might pave the way for future investigations on quantum machine learning techniques especially based on hybrid quantum technologies., Comment: 9 pages, 7 figures

Frequency correlations are a versatile and powerful tool which can be exploited to perform spectral analysis of objects whose direct measurement might be unfeasible. This is achieved through a so-called ghost spectrometer, that can be implemented with quantum and classical resources alike. While there are some known advantages associated to either choice, an analysis of their metrological capabilities has not yet been performed. Here we report on the metrological comparison between a quantum and a classical ghost spectrometer. We perform the estimation of the transmittivity of a bandpass filter using frequency-entangled photon pairs. Our results show that a quantum advantage is achievable, depending on the values of the transmittivity and on the number of frequency modes analyzed.

Calibration of sensors is a fundamental step to validate their operation. This can be a demanding task, as it relies on acquiring a detailed modelling of the device, aggravated by its possible dependence upon multiple parameters. Machine learning provides a handy solution to this issue, operating a mapping between the parameters and the device response, without needing additional specific information on its functioning. Here we demonstrate the application of a Neural Network based algorithm for the calibration of integrated photonic devices depending on two parameters. We show that a reliable characterization is achievable by carefully selecting an appropriate network training strategy. These results show the viability of this approach as an effective tool for the multiparameter calibration of sensors characterized by complex transduction functions.

Characterizing a system often demands learning its response function to an applied field. Such knowledge is rooted on the experimental evaluation of punctual fiducial response and interpolation to access prediction at arbitrary values. Quantum metrological resources are known to provide enhancement in assessing these fiducial points, but the implications for improved function estimation have only recently been explored, and have not been yet demonstrated. Here we show an experimental realization of function estimation based on a photonic achitecture. The phase response of a liquid-crystal to a voltage has been reconstructed by means of quantum and classical phase estimation, providing evidence of the superiority of the former and highlighting the interplay between punctual statistical error and interpolation error. Our results show how quantum resources should successfully be employed to access the rich information contained in continuous signals.

We present an experimental method to detect lower bounds to the quantum capacity of two-qubit communication channels. We consider an implementation with polarisation degrees of freedom of two photons and report on the efficiency of such a method in the presence of correlated noise for varying values of the correlation strength. The procedure is based on the generation of separable states of two qubits and local measurements at the output. We also compare the performance of the correlated two-qubit channel with the single-qubit channels corresponding to the partial trace on each of the subsystems, thus showing the beneficial effect of properly taking into account correlations to achieve a larger quantum capacity.

Multiphase estimation is a paradigmatic example of a multiparameter problem. When measuring multiple phases embedded in interferometric networks, specially-tailored input quantum states achieve enhanced sensitivities compared with both single-parameter and classical estimation schemes. Significant attention has been devoted to defining the optimal strategies for the scenario in which all of the phases are evaluated with respect to a common reference mode, in terms of optimal probe states and optimal measurement operators. As well, the strategies assume unlimited external resources, which is experimentally unrealistic. Here, we optimize a generalized scenario that treats all of the phases on an equal footing and takes into account the resources provided by external references. We show that the absence of an external reference mode reduces the number of simultaneously estimatable parameters, owing to the immeasurability of global phases, and that the symmetries of the parameters being estimated dictate the symmetries of the optimal probe states. Finally, we provide insight for constructing optimal measurements in this generalized scenario. The experimental viability of this work underlies its immediate practical importance beyond fundamental physics., Comment: 11 pages, 2 figures, 1 table; comments welcome!

Non-equilibrium states of quantum systems in contact with thermal baths help telling environments with different temperatures or different statistics apart. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that non-equilibrium states are not universally optimal, and detail the conditions in which it becomes convenient to wait for complete thermalisation of the probe. These concepts are illustrated in a linear optical simulation., Comment: Few typos corrected, bibliography expanded

Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally for the first time an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources., Comment: 10+4 pages, 6+2 figures

We characterize the energetic footprint of a two-qubit quantum gate from the perspective of non-equilibrium quantum thermodynamics. We experimentally reconstruct the statistics of energy and entropy fluctuations following the implementation of a controlled-unitary gate, linking them to the performance of the gate itself and the phenomenology of Landauer principle at the single-quantum level. Our work thus addresses the energetic cost of operating quantum circuits, a problem that is crucial for the grounding of the upcoming quantum technologies., Comment: This version matches the published article

Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated parameter. When Bayesian techniques are adopted, more elements become available for assessing the quality of the estimation. Here we adopt generalized classical Cram\'er-Rao bounds for looking in detail into a phase-estimation experiment performed with quantum light. In particular, we show that the third-order absolute moment can give a superior capability in revealing biases in the estimation, compared to standard approaches. Our studies point to the identification of an alternative strategy that brings a possible advantage in monitoring the correct operation of high-precision sensors., Comment: 6 pages, 5 figures

Encoding information in the time-frequency domain is demonstrating its potential for quantum information processing. It offers a novel scheme for communications with large alphabets, computing with large quantum systems, and new approaches to metrology. It is then crucial to secure full control on the generation of time-frequency quantum states and their properties. Here, we present an overview of the theoretical background and the technical aspects related to the characterization of time-frequency properties of two-photon states. We provide a detailed account of the methodologies which have been implemented for measuring frequency correlations and for the retrieval of the full spectral wavefunction. This effort has benefited enormously from the adaptation of classical metrology schemes to the needs of operating at the single-photon level.

The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments., Comment: 14 pages, 1 figure. Comments are welcome

Quantum sensors are among the most promising quantum technologies, allowing to attain the ultimate precision limit for parameter estimation. In order to achieve this, it is required to fully control and optimize what constitutes the hardware part of the sensors, i.e. the preparation of the probe states and the correct choice of the measurements to be performed. However careful considerations must be drawn also for the software components: a strategy must be employed to find a so-called optimal estimator. Here we review the most common approaches used to find the optimal estimator both with unlimited and limited resources. Furthermore, we present an attempt at a more complete characterization of the estimator by means of higher-order moments of the probability distribution, showing that most information is already conveyed by the standard bounds.

Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models can account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case of qubits. We show that when performing generic postselected measurements there exist no one-to-one mapping between them, an instance that leads to drawing more involved considerations.

Enzymes are essential to maintain organisms alive. Some of the reactions they catalyze are associated with a change in reagents chirality, hence their activity can be tracked by using optical means. However, illumination affects enzyme activity: the challenge is to operate at low-intensity regime avoiding loss in sensitivity. Here we apply quantum phase estimation to real-time measurement of invertase enzymatic activity. Control of the probe at the quantum level demonstrates the potential for reducing invasiveness with optimized sensitivity at once. This preliminary effort, bringing together methods of quantum physics and biology, constitutes an important step towards full development of quantum sensors for biological systems.

Introducing quantum sensors as solution to real-world problem demands reliability and controllability outside laboratory conditions. Producers and operators ought to be assumed to have limited resources ready available for calibration, and yet, they should be able to trust the devices. Neural networks are almost ubiquitous for similar tasks for classical sensors: here we show the applications of this technique to calibrating a quantum photonic sensor. This is based on a set of training data, collected only relying on the available probe states, hence reducing overheads. We found that covering finely the parameter space is key to achieve uncertainties close to their ultimate level. This technique has potential to become the standard approach to calibrate quantum sensors.

The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology., Comment: close to published version

Exploitation of time-frequency properties of SPDC photon pairs has recently found application in many endeavors. Complete characterization and control over the states in this degree of freedom is of paramount importance for the development of optical quantum technologies. This is achieved by accessing information both on the joint spectral amplitude and the joint spectral phase. Here we propose a novel scheme based on the MICE algorithm, which aims at reconstructing the joint spectral phase by adopting a multi-shear approach, making the technique suitable for noisy environments. We report on simulations for the phase reconstruction and propose an experiment using a Franson modified interferometer.

Quantum photonics has demonstrated its potential for enhanced sensing. Current sources of quantum light states tailored to measuring, allow to monitor phenomena evolving on time scales of the order of the second. These are characteristic of product accumulation in chemical reactions of technologically interest, in particular those involving chiral compounds. Here we adopt a quantum multiparameter approach to investigate the dynamic process of sucrose acid hydrolysis as a test bed for such applications. The estimation is made robust by monitoring different parameters at once.

Classifying quantum states usually demands to observe properties such as the amount of correlation at one point in time. Further insight may be gained by inspecting the dynamics in a given evolution scheme. Here we attempt such a classification looking at single-qubit and two-qubit states at the start of thermalisation with a heat bath. The speed with which the evolution starts is influenced by quantum aspects of the state, however, such signatures do not allow for a systematic classification.

The simplicity of a question such as wondering if correlations characterize or not a certain system collides with the experimental difficulty of accessing such information. Here we present a low demanding experimental approach which refers to the use of a metrology scheme to obtain a conservative estimate of the strength of frequency correlations. Our testbed is the widespread case of a photon pair produced per downconversion. The theoretical architecture used to put the correlation degree on a quantitative ground is also described.

Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however the best precision is achieved outside equilibrium condition. Here, we discuss a way to generalize this relation in a non-equilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation., Comment: 7 pages, 4 figures

Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a multiparameter approach, in which noise is associated to a parameter to be measured at the same time as the phase. We present an experiment using two-photon states, and apply our setup to investigating optical activity of fructose solutions. Finally, we illustrate the scaling laws of the attainable precisions with the number of photons in the probe state.

The emergence of realistic properties is a key problem in understanding the quantum-to-classical transition. In this respect, measurements represent a way to interface quantum systems with the macroscopic world: these can be driven in the weak regime, where a reduced back-action can be imparted by choosing meter states able to extract different amounts of information. Here we explore the implications of such weak measurement for the variation of realistic properties of two-level quantum systems pre- and post-measurement, and extend our investigations to the case of open systems implementing the measurements.

Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on the thermodynamics of the information erasure. Limits of the applicability of our bounds are discussed, and demonstrated in a quantum photonic simulator.

The physics that governs quantum monitoring may involve other degrees of freedom than the ones initialised and controlled for probing. In this context we address the simultaneous estimation of phase and dephasing characterizing a dispersive medium, and we explore the role of frequency correlations within a photon pair generated via parametric down-conversion, when used as a probe for the medium. We derive the ultimate quantum limits on the estimation of the two parameters, by calculating the corresponding quantum Cram\'er-Rao bound; we then consider a feasible estimation scheme, based on the measurement of Stokes operators, and address its absolute performances in terms of the correlation parameters, and, more fundamentally, of the role played by correlations in the simultaneous achievability of the quantum Cram\'er-Rao bounds for each of the two parameters., Comment: to appear in Quantum Measurements and Quantum Metrology

We experimentally demonstrate a source of nearly pure single photons in arbitrary temporal shapes heralded from a parametric down-conversion (PDC) source at telecom wavelengths. The technology is enabled by the tailored dispersion of in-house fabricated waveguides with shaped pump pulses to directly generate the PDC photons in on-demand temporal shapes. We generate PDC photons in Hermite-Gauss and frequency-binned modes and confirm a minimum purity of 0.81, even for complex temporal shapes.

The metrological ability of carefully designed probes can be spoilt by the presence of noisy processes occurring during their evolution. The noise is responsible for altering the evolution of the probes in such a way that bear little or no information on the parameter of interest, hence spoiling the signal-to-noise ratio of any possible measurement. Here we show an experiment in which the introduction of an ancilla improves the estimation of an optical phase in the high-noise regime. The advantage is realised by the coherent coupling of the probe and the ancilla at the initialisation and the measurement state, which generate and then select a subset of overall configurations less affected by the noise process.