Quantum clocks and their synchronisation - the Alternate Ticks Game

Abstract: Time plays a crucial role in the intuitive understanding of the world around us. Within quantum mechanics, however, time is not usually treated as an observable quantity; it enters merely as a parameter in the laws of motion of physical systems. Here we take an operational approach to time. Towards this goal we consider quantum clocks, i.e., quantum systems that generate an observable time scale. We then study the quality of quantum clocks in terms of their ability to stay synchronised. To quantify this, we introduce the "Alternate Ticks Game" and analyse a few strategies pertinent to this game.