Entanglement and its relationship to classical dynamics

Abstract

We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement SQ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of SQ even for the extreme case of two spin-1/2 qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.

Quantum signatures of chaos, thermalization, and tunneling in the exactly solvable few-body kicked top

“…Note that for κ 0 that are multiples of 2πj, U is a local operator and does not create entanglement, we therefore restrict attention to the interval κ 0 ∈ [0, πj]. The case of 2-qubits, j = 1, has been analyzed in [49] wherein interesting arguments have been proposed for the observation of structures not linked to the classical limit. In this case, several quantum correlation measures were also calculated in [50].…”

Periodicity of quantum correlations in the quantum kicked top

“…Quite remarkably, ergodic behaviour in this isolated quantum systems was demonstrated [19]. Surprisingly, a recent theoretical work has shown that even in the deep quantum limit possible with just two qubits, the system appears to take into account the nature of classical dynamics in the vicinity of the phase space coordinates where the spin coherent state is initially placed [7]. Further, this work also hints that the entanglement entropy might display (quasi-)periodic behaviour in time and also as a function of kick strength.…”

“…Measures of quantum correlations have been found to strongly correlate with the qualitative nature of classical phase space, whether it is regular or chaotic [3,7,9,14,17,18]. In general, as demonstrated extensively in a series of papers using * udaybhosale0786@gmail.com † santh@iiserpune.ac.in kicked tops [2,3,7,9,14,[17][18][19], the qualitative nature and details of classical dynamics influences entanglement. In addition, classical dynamical features such as the bifurcation also affect the quantum correlation measures with interesting semiclassical consequences [3].…”

Effect of system energy on quantum signatures of chaos in the two-photon Dicke model

“…Moreover, the study of entanglement entropy indicates that in general the chaotic systems tend to own larger entanglement entropy than the regular systems [7][8][9][10][11]. However, the correspondence relationship between entanglement entropy and chaos is not always hold since there exist certain cases in which the entanglement entropy for the initial state prepared in the regular region is higher than that of in chaotic region [12][13][14]. The intrinsic physics is still uncertain and needs to be further investigated.…”

“…Recently, Ruebeck et al [14] studied the entangling quantum kicked top and divided the infinite-time-averaged entanglement entropy S Q into two parts: I Q and R Q , which come respectively from the "diagonal" and "offdiagonal" matrix elements of the angular momentum operators obtained by the Floquet eigenstates of the system. They found that I Q and S Q were correlated with a quantity I c , which is not equivalent to classical chaos.…”