In this review we present the potentialities and the achievements of the use of non-classical photon-number correlations in twin-beam states for many applications, ranging from imaging to metrology. Photon-number correlations in the quantum regime are easily produced and are rather robust against unavoidable experimental losses, and noise in some cases, if compared to the entanglement, where losing one photon can completely compromise the state and its exploitable advantages. Here, we will focus on quantum enhanced protocols in which only phase-insensitive intensity measurements (photon-number counting) are performed, which allow probing the transmission/absorption properties of a system, leading, for example, to innovative target detection schemes in a strong background. In this framework, one of the advantages is that the sources experimentally available emit a wide number of pair-wise correlated modes, which can be intercepted and exploited separately, for example by many pixels of a camera, providing a parallelism, essential in several applications, such as wide-field sub-shot-noise imaging and quantum enhanced ghost imaging. Finally, non-classical correlation enables new possibilities in quantum radiometry, e.g. the possibility of absolute calibration of a spatial resolving detector from the on-off single-photon regime to the linear regime in the same setup.

One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.

Weak value measurements have recently given rise to a great amount of interest in both the possibility of measurement amplification and the chance for further quantum mechanics foundations investigation. In particular, a question emerged about weak values being proof of the incompatibility between quantum mechanics and noncontextual hidden variables theories (NCHVTs). A test to provide a conclusive answer to this question was given by Pusey [Phys. Rev. Lett. 113, 200401 (2014)], where a theorem was derived showing the NCHVT incompatibility with the observation of anomalous weak values under specific conditions. In this Letter we realize this proposal, clearly pointing out the connection between weak values and the contextual nature of quantum mechanics.

Loss measurements are at the base of spectroscopy and imaging, thus permeating all the branches of science, from chemistry and biology to physics and material science. However, quantum mechanics laws set the ultimate limit to the sensitivity, constrained by the probe mean energy. This can be the main source of uncertainty, for example when dealing with delicate systems such as biological samples or photosensitive chemicals. It turns out that ordinary (classical) probe beams, namely with Poissonian photon number distribution, are fundamentally inadequate to measure small losses with the highest sensitivity. It is known that quantum-correlated pair of beams, named “twin-beam state”, allows surpassing this classical limit. Here we demonstrate they can reach the ultimate sensitivity for all energy regimes (even less than one photon per mode) with the simplest measurement strategy. One beam of the pair addresses the sample, while the second one is used as a reference to compensate both for classical drifts and for fluctuation at the most fundamental quantum level. This capability of selfcompensating for unavoidable instability of the sources and detectors allows also to strongly reduce the bias in practical measurement. Moreover, we report the best sensitivity per photon ever achieved in loss estimation experiments.

We show how the same setup and procedure, exploiting spatially multimode quantum correlations, allows the absolute calibration of an electron-multiplying charge-coupled (EMCCD) camera from the analog regime down to the single-photon-counting level, just by adjusting the brightness of the quantum source. At the single-photon level, an EMCCD can be operated as an on–off detector, where quantum efficiency depends on the discriminating threshold. We develop a simple model to explain the connection of the two different regimes demonstrating that the efficiency estimated in the analog (bright) regime allows us to accurately predict the detector behavior in the photocounting regime and vice versa. This work establishes a bridge between two regions of the optical measurements that up to now have been based on completely different standards, detectors, and measurement techniques.