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 $\mathrm{QBER}=4.6\%$ for a total link duration of 85 s. The mean photon number per pulse ${\mu }_{\text{sat}}$ 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.

Establishing secure communication links at a global scale is a major potential application of quantum information science but also extremely challenging for the underlying technology. Although milestone experiments using satellite-to-ground links and exploiting singe-photon encoding for implementing quantum key distribution have shown recently that this goal is achievable, it is still necessary to further investigate practical solutions compatible with classical optical communication systems. Here, we examine the feasibility of establishing secret keys in a satellite-to-ground downlink configuration using continuous-variable encoding, which can be implemented using standard telecommunication components certified for space environment and able to operate at high symbol rates. Considering a realistic channel model and state-of-the-art technology, and exploiting an orbit subdivision technique for mitigating fluctuations in the transmission efficiency, we find positive secret key rates for a low-Earth-orbit scenario, whereas finite-size effects can be a limiting factor for higher orbits. Our analysis determines regions of values for important experimental parameters where secret key exchange is possible and can be used as a guideline for experimental efforts in this direction.

Quantum interference arising from the superposition of states is striking evidence of the validity of quantum mechanics, confirmed in many experiments and also exploited in applications. However, as for any scientific theory, quantum mechanics is valid within the limits in which it has been experimentally verified. In order to extend such limits, it is necessary to observe quantum interference in unexplored conditions such as moving terminals at large distances in space. Here, we experimentally demonstrate single photon interference at a ground station due to the coherent superposition of two temporal modes reflected by a rapidly moving satellite a thousand kilometers away. The relative speed of the satellite induces a varying modulation in the interference pattern. The measurement of the satellite distance in real time by laser ranging allows us to precisely predict the instantaneous value of the interference phase. We then observed the interference patterns with a visibility up to 67% with three different satellites and with a path length up to 5000 km. Our results attest to the viability of photon temporal modes for fundamental 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 wave function [J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function 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 original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.