Quantum communication (QC), namely, the faithful transmission of generic quantum states, is a key ingredient of quantum information science. Here we demonstrate QC with polarization encoding from space to ground by exploiting satellite corner cube retroreflectors as quantum transmitters in orbit and the Matera Laser Ranging Observatory of the Italian Space Agency in Matera, Italy, as a quantum receiver. The quantum bit error ratio (QBER) has been kept steadily low to a level suitable for several quantum information protocols, as the violation of Bell inequalities or quantum key distribution (QKD). Indeed, by taking data from different satellites, we demonstrate an average value of QBER=4.6% for a total link duration of 85 s. The mean photon number per pulse μ_{sat} leaving the satellites was estimated to be of the order of one. In addition, we propose a fully operational satellite QKD system by exploiting our communication scheme with orbiting retroreflectors equipped with a modulator, a very compact payload. Our scheme paves the way toward the implementation of a QC worldwide network leveraging existing receivers.

Quantum interference arising from the superposition of states is striking evidence of the validity of\ud quantum mechanics, confirmed in many experiments and also exploited in applications. However, as for\ud any scientific theory, quantum mechanics is valid within the limits in which it has been experimentally\ud verified. In order to extend such limits, it is necessary to observe quantum interference in unexplored\ud conditions such as moving terminals at large distances in space. Here, we experimentally demonstrate\ud single photon interference at a ground station due to the coherent superposition of two temporal modes\ud reflected by a rapidly moving satellite a thousand kilometers away. The relative speed of the satellite\ud induces a varying modulation in the interference pattern. The measurement of the satellite distance in real\ud time by laser ranging allows us to precisely predict the instantaneous value of the interference phase. We\ud then observed the interference patterns with a visibility up to 67% with three different satellites and with a\ud path length up to 5000 km. Our results attest to the viability of photon temporal modes for fundamental\ud tests of physics and quantum communication in space

Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wavefunction [Nature (London) 474, 188 (2011)]. Here we show that direct measurement of the wavefunction can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e. those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the reconstructed and original wavefunctions obtained by the weak measurement approach: this will allow to define the range of applicability of such method.

Open questions are still present in fundamental Physics and Cosmology, like the nature of Dark Matter, the matter-antimatter asymmetry and the validity of the particle