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.

We address the quantum characterization of photon counters based on transition-edge sensors (TESs) and present the first experimental tomography of the positive operator-valued measure (POVM) of a TES. We provide the reliable tomographic reconstruction of the POVM elements up to 11 detected photons and M = 100 incoming photons, demonstrating that it is a linear detector.

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.

We present a heralded single-photon source with a much lower level of unwanted background photons in the output channel by using the herald photon to control a shutter in the heralded channel. The shutter is implemented using a simple field programable gate array controlled optical switch.

Low noise single-photon sources are a critical element for quantum technologies. We present a heralded single-photon source with an extremely low level of residual background photons, by implementing low-jitter detectors and electronics and a fast custom-made pulse generator controlling an optical shutter (a ${\text{LiNbO}}_3$ waveguide optical switch) on the output of the source. This source has a second-order autocorrelation $g^{(2)}(0)=0.005(7)$ , and an output noise factor (defined as the ratio of the number of noise photons to total photons at the source output channel) of 0.25(1)%. These are the best performance characteristics reported to date.