Symmetries and Synchronization Blockade

TL;DR

This paper investigates how Hamiltonian symmetries and the choice of synchronization measures influence the phenomenon of synchronization blockade in quantum systems, providing theoretical proofs and illustrative examples.

Contribution

It introduces a general theorem showing synchronization blockade cannot occur in full $SU(N)$ systems and explores how different measures can detect blockade-like behavior.

Findings

Synchronization blockade is absent in full $SU(N)$ systems with certain states.

Information-theoretic measures can also observe blockade-like phenomena.

The choice of synchronization measure affects the detection of blockade.

Abstract

Synchronization blockade refers to an interferometric cancellation of quantum synchronization. In this manuscript, 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 $SU(N)$ group. We present several illustrative examples of synchronization blockade in multi-level 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.