Bipartite Bell inequalities can be simultaneously violated by two different pairs of observers when weak measurements and signaling is employed. Here we experimentally demonstrate the violation of two simultaneous CHSH inequalities by exploiting a two-photon polarization maximally entangled state. Our results demonstrate that large double violation is experimentally achievable. Our demonstration may have impact for Quantum Key Distribution or certification of Quantum Random Number generators based on weak measurements.

Satellite-based quantum communication is an invaluable resource for the realization of a quantum network at the global scale. In this regard, the use of satellites well beyond the low Earth orbits gives the advantage of long communication time with a ground station. However, high-orbit satellites pose a great technological challenge due to the high diffraction losses of the optical channel, and the experimental investigation of such quantum channels is still lacking. Here, we report on the first experimental exchange of single photons from Global Navigation Satellite System at a slant distance of 20000 kilometers, by exploiting the retroreflector array mounted on GLONASS satellites. We also observed the predicted temporal spread of the reflected pulses due to the geometrical shape of array. Finally, we estimated the requirements needed for an active source on a satellite, aiming towards quantum communication from GNSS with state-of-the-art technology.

Widespread adoption of Quantum Key Distribution (QKD) in current telecommunication networks will require the development of simple, low cost and stable systems. Current QKD implementations usually include separate sub-systems to implement auxiliary tasks such as temporal synchronization and polarization basis tracking. Here we present a QKD system with polarization encoding that performs synchronization, polarization compensation and QKD with the same optical setup without requiring any changes or any additional hardware. Polarization encoding is performed by a self-compensating Sagnac loop modulator which exhibits high stability and the lowest intrinsic QBER ever reported by an active polarization source fully implemented using only commercial offthe-shelf components. We tested our QKD system over a fiber-optic channel, tolerating up to 43 dB of total losses and representing an important step towards technologically mature QKD systems. * These authors contributed equally to this work.

New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only O(d) different operations, compared to d 2 linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors.