Entanglement as a signature of quantum chaos

Abstract

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter $κ$ in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both bipartite and pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as $κ$ moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over initial states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.