Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

Abstract

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. Measures of quantum correlations do not have a classical analog and yet are influenced by classical dynamics. In this work, by modeling the quantum kicked top as a multiqubit system, the effect of classical bifurcations on measures of quantum correlations such as the quantum discord, geometric discord, and Meyer and Wallach Q measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of trivial fixed points of the kicked top, the scaling function decays as a power law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the Q measure. We also suggest that it can have experimental consequences.

Quantum-classical correspondence in the vicinity of periodic orbits

“…Signatures of chaos have been widely studied in the quantum kicked top using various quantum theoretic measures in the deep quantum regime as well as the semi-classical regime [18,[21][22][23][24][25][26][27]. Our analysis and criteria for quantum-classical correspondence can be applied to understand these previous results and develop better quantum control techniques.…”

Star-topology Registers: NMR and Quantum Information Perspectives

“…One of the most extensively studied models of chaos is the kicked top model [88][89][90][91][92][93]. Krithika et al had [87] used a two-qubit system to investigate quantum chaos in the kicked top.…”

Statistical complexity of the kicked top model considering chaos

“…Therefore this model is an important area of research [9,33,42,52] for the study of entanglement [37,24,45,34,4,60] and its relationship to classical dynamics [57], sign of bifurcations on different quantum correlation measures [9], quantum classical transition with respect to periodic trajectories [33] and the behavior of entropy in the transition to chaos citezs. Measure of quantum correlations is strongly correlated with the qualitative nature of classical phase space, whether it is regular or chaotic [9,52,37,3,41,20,62]. The importance of the kicked top model is also demonstrated by the large number in a series of papers [14,9,52,37,3,41,20,47,10].…”

“…Measure of quantum correlations is strongly correlated with the qualitative nature of classical phase space, whether it is regular or chaotic [9,52,37,3,41,20,62]. The importance of the kicked top model is also demonstrated by the large number in a series of papers [14,9,52,37,3,41,20,47,10].…”

“…first consider the system at p = π 2 . It was studied by wide range of articles [9,33,3,41,47,28] in the literature. Due to newer symmetries, the shape of the mapping is simplified as follows…”