Polarization Transformations on Qubits in a Earth-to-Space Quantum Communication System Involving Galileo Satellites
Bonato, C.¹; Occhipinti, T.¹; Pernechele, C.²; Barbieri, C.¹; Villoresi, P.^1
1Universita' di Padova; ²INAF Cagliari, Capoterra

Space-based technology could offer the opportunity to reach global-scale quantum networking since it allows a much larger propagation distance of photonic qubits, as compared to both fiber and terrestrial free-space links. Here we investigate the possibility of employing Galileo satellites to implement a quantum communication link between Earth and Space.

One of the most widespread implementations of qubits for quantum communication is polarization-encoding, for which it is crucial to have a shared reference frame between the communication parties, so as to be able to transmit and receive the polarization states correctly. If the satellite is not geostationary, any spatial reference frame between a Space-born transmitter and Earth-based receiver will be modified due to the movement of the involved pointing and tracking mirrors. This, combined with the reflection on mirrors, will introduce a time-dependent polarization transformation, which is important to estimate in order to properly design a compensation system.

If we consider an example of a passage of a Galileo satellite, the Stokes parameters received at the ground station (for a given input vertically-polarized state) change with time as shown in Fig. 1. The velocity of variation can be seen, looking at the time derivative, in Fig. 2.

This effect is therefore dramatic, and it is much more important than the atmospheric effects (turbulence, scattering processes or Faraday effect), both because it is time-dependent and because of its magnitude.

According to theoretical models and experimental data, turbulence could give a rotation of the order of 10-11 rad/Km, while scattering could contribute with a rotation of about 10-4 rad/Km. The rotation induced by the Earth’s magnetic field, through Faraday effect, is well below 10-3 rad.

Our results show that an active compensation system is needed, since for quantum communication all the polarization states must be transmitted and received correctly. A first approach could be to deterministically calculate the polarization rotation in real time, knowing the satellite position and the mirrors’ angles. This approach requires that all the relevant parameters of the each mirror are known and stable against physical fluctuations. A second possible implementation could be by means of a reference laser at a different wavelength with respect to the signal photons, from which the time-dependent instrumental polarization transformation could be retrieved. The problem is that, the transformations induced on different wavelengths are not identical, so the compensation could not be perfect. Another possible approach could be a time-multiplexing configuration, alternating the times where the signal and the reference photons are emitted. This scheme, provided that the transmission and analysis of the reference beam is repeated at sufficiently high rate to keep up with the temporal variations of the channel, will allow near perfect compensation, but will extremely slow down the transmission if the coherence time of the channel is low. But, in the case of Galileo satellites, the changes are quite slow, making this the best approach for compensation. In conclusion, our study addressed the issues of the optical link to Galileo satellites in terms of the feasibility of a quantum channel.