Asynchronisation is a major limiting factor for Coordinated Universal time (UTC) performance, and, by extension, other clock-network concepts, and our aim is to quantify asynchronisation reliably between different local representations of UTC, known as UTC(k) for k the site label. To this end, we devise a simple but faithful physical model and mathematical description for quantifying asynchronisation reliably between different UTC(k). Our UTC mathematical model comprises coupled Ornstein-Uhlenbeck (OU) processes, each representing UTC(k), which we discuss physically as a network of ballistic clocks network managed by a controller; for clarity we illustrate this network in the context of the sport of curling with the ballistic clocks pictured as curling stones. From our closed-form solution, we establish how to quantify asynchronisation reliably. Furthermore, we extend our ballistic-clock model to accommodate quantum effects, namely squeezing and entanglement, and analyse potential quantum advantage. Our approach to reliably quantifying asynchronisation is an important step forward conceptually for UTC to serve as a common time reference for Global Navigation Satellite System (GNSS) interoperability.