Energy-Efficient Satellite Wake-Up via Bosonic Identification: The Role of Synchronization

Abstract: The information-theoretic concept of identification describes a sender-receiver architecture in which the receiver only checks whether a particular message was sent or not, thereby promising a low-energy receiver design. In low received-energy regimes, quantum receivers are a promising tool for studying the system limits. However, the known information-theoretically optimal identification codes typically assume perfect synchronization. In this work, we study deterministic identification in a satellite setting under explicit synchronization constraints, where a satellite broadcasts the signature of a specific User Equipment (UE) which it assumes to be attached to one out of several possible Ground Station (GS), with the goal of establishing communication with the target UE. Within the proposed design, and assuming a specific phase-encoded coherent-state clock scheme in which the discrete time index is represented by equidistant phase rotations on the unit circle, our results reveal a fundamental asymmetry: At any transmission power, identification performance improves with blocklength, whereas synchronization accuracy degrades. In particular, the energy needed for transmitting the satellite clock to the GS can be several orders of magnitude higher than the one needed for the identification signal. This indicates that synchronization strongly impacts identification performance and motivates the investigation of the error-correcting capabilities of bosonic codes under jitter.