Importance of time and frequency reference in quantum astronomy and quantum communications

Very accurate and stable time tagging capabilities are fundamental for Quantum Astronomy and Quantum Key Distribution. The main task of Quantum Astronomy is to find particular signatures of different astrophysical emission mechanisms or scattering processes by measuring the statistics of the arrival time of each incoming photon. This line of research will be particularly important with future extremely large telescopes. On the other hand, Quantum Key Distribution (QKD) assures a secure cryptographic key sharing between optical transmitters and receivers through the synchronous exchange of quantum states (e.g., single polarized photons). Both technologies need to detect the arrival times each photon with very high temporal resolution in order to discriminate the signal photons from the background ones. In this article, we present the activities of our research group on Quantum Astronomy and Quantum Key Distribution, taking into account their very strict requirements. For Quantum Astronomy, we have developed an instrument called AquEYE capable of time-tagging each incoming single photon using as detectors four Single Photon Avalanche Diodes (SPAD). In this experiment, we need to maintain an absolute time scale reference with a maximum error phase less than 1 ns for measurements lasting more than 30 minutes. For the development phase of our instrument, we used an available rubidium oscillator disciplined by a GPS receiver. This system will supply the reference clock and trigger signal to our acquisition electronics, which are based on a time-to-digital converter. In the paper, we will present the more advanced solution we have under evaluation. As we are also working in the realization of a QKD prototype, we will present our study on time and frequency stability of the local oscillators of the electronics. For the moment, we are using two simple quartzes, but in the article we will show the results of several mathematical simulations. With them, we will analyze the performance tradeoffs in terms of the final cryptographic key rate, through different synchronization techniques and frequency reference sources.