Generalized entanglement as a natural framework for ex - ploring quantum chaos

– We demonstrate that generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)] provides a natural and reliable indicator of quantum chaotic behavior. Since generalized entanglement depends directly on a choice of preferred observables, exploring how generalized entanglement increases under dynamical evolution is possible without invoking an auxiliary coupled system or decomposing the system into arbitrary subsystems. We find that, in the chaotic regime, the long-time saturation value of generalized entanglement agrees with random matrix theory predictions. For our system, we provide physical intuition into generalized entanglement within a single system by invoking the notion of extent of a state. The latter, in turn, is related to other signatures of quantum chaos. Central to the study of quantum chaos [1] and broadly significant to fundamental quantum theory [2], is the determination of distinctive signatures that unambiguously identify quantum systems whose classical limit exhibits chaotic, versus regular, dynamics. Such signatures are discovered by contrasting quantized versions of classically chaotic and non-chaotic systems. A well-established static signature of quantum chaos is the accurate description of a chaotic operators' eigenvalue and eigenvector element statistics by random matrix theory (RMT) [1,3]. A dynamic indicator of quantum chaos is the fidelity decay behavior [4–10]. While both approaches have led to deep insights into quantum chaos and its relation to the underlying classical dynamics, they suffer from intrinsic weaknesses. Eigenvector statistics, for example, is basis-dependent. The effectiveness of fidelity decay as an indicator of quantum chaos is strongly influenced by the form of the perturbation. Indeed, regular systems may show chaotic fidelity decay behavior depending on the type of perturbation [8]. A signature of quantum chaos which need not be subject to the above weaknesses and is very natural from a quantum information standpoint is entanglement generation. Chaotic evolution tends to produce states whose statistical properties are similar to those of random pure states. Because such states tend to be highly entangled [11], we expect that quantum