Experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams are reported. Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood estimation and does not involve photon counting. Reconstructions of the distribution for both semiclassical and quantum states of light are reported for single-mode as well as for multimode beams.

In the last years several theoretical papers discussed if time can be an emergent propertiy deriving from quantum correlations. Here, to provide an insight into how this phenomenon can occur, we present an experiment that illustrates Page and Wootters' mechanism of "static" time, and Gambini et al. subsequent refinements. A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. We implement this mechanism using an entangled state of the polarization of two photons, one of which is used as a clock to gauge the evolution of the second: an "internal" observer that becomes correlated with the clock photon sees the other system evolve, while an "external" observer that only observes global properties of the two photons can prove it is static."Quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio." [1] The "problem of time" [2][3][4][5][6] in essence stems from the fact that a canonical quantization of general relativity yields the Wheeler-De Witt equation [7,8] predicting a static state of the universe, contrary to obvious everyday evidence. A solution was proposed by Page and Wootters [9, 10]: thanks to quantum entanglement, a static system may describe an evolving "universe" from the point of view of the internal observers. Energy-entanglement between a "clock" system and the rest of the universe can yield a stationary state for an (hypothetical) external observer that is able to test the entanglement vs. abstract coordinate time. The same state will be, instead, evolving for internal observers that test the correlations between the clock and the rest [9][10][11][12][13][14]. Thus, time would be an emergent property of subsystems of the universe deriving from their entangled nature: an extremely elegant but controversial idea [2,15]. Here we want to demystify it by showing experimentally that it can be naturally embedded into (small) subsystems of the universe, where Page and Wootters' mechanism (and Gambini et al. subsequent refinements [12,16]) can be easily studied. We show how a static, entangled state of two photons can be seen as evolving by an observer that uses one of the two photons as a clock to gauge the time-evolution of the other photon. However, an external observer can show that the global entangled state does not evolve.Even though it revolutionizes our ideas on time, Page and Wootters' (PaW) mechanism is quite simple [9-11]: they provide a static entangled state |Ψ whose subsystems evolve according to the Schrödinger equation for an observer that uses one of the subsystems as a clock system C to gauge the time evolution of the rest R. While the division into subsystems is largely arbitrary, the PaW model assumes the possibility of neglecting interaction among them writing the Hamiltonian of the global system as H = H c ⊗ 1 1 r + 1 1 c ⊗ H r , where H c , H r are the local terms associated with C and R, respectively and Uc(t) = e −iHct/ are the ...

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.

One description provides only probabilities for obtaining various eigenvalues of a quantum variable. The eigenvalues and the corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property of an ensemble of quantum systems. In contrast to this paradigm, here we demonstrate a method for measuring the expectation value of a physical variable on a single particle, namely, the polarization of a single protected photon. This realization of quantum protective measurements could find applications in the foundations of quantum mechanics and quantum-enhanced measurements

Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.