Synchronize accelerated clock in a multipartite relativistic quantum system

Abstract

We perform a protocol for multipartite quantum clock synchronization under the influence of Unruh thermal noise. The clocks consisting of Unruh-DeWitt detectors when one of detectors accelerated is obtained. To estimate the time difference between the clocks, we calculate the time probability and analyze how the probability is influenced by the Unruh thermal noise and other factors. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach to the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two-party system is always higher than in an multipartite system, while the optimal $Z$-type multipartite initial state always perform better than the $W$-type state.