Symmetries and synchronization blockade

Abstract

Synchronization blockade refers to an interferometric cancellation of quantum synchronization. In this paper, we show how the choice of synchronization measure and Hamiltonian symmetries affect the discussion of synchronization blockade. Using counting principles, we prove a general theorem that synchronization blockade cannot be observed in an $N$-level system when the coherent state used to define the diagonal limit-cycle state is in the full $\text{SU}(N)$ group. We present several illustrative examples of synchronization blockade in multilevel systems and prove that information-theoretic measures of synchronization can also observe synchronization-blockade-like behavior by an appropriate choice of the set of limit-cycle states.