Generalized entanglement as a natural framework for exploring quantum chaos

¹ Quantum Information Science Group, Mitre - Eatontown, NJ 07724, USA
² Department of Physics and Astronomy, Dartmouth College - Hanover NH 03755, USA

Corresponding authors: weinstein@mitre.org lorenza.viola@dartmouth.edu

Received: 25 July 2006
Accepted: 9 October 2006

Abstract

We demonstrate that generalized entanglement (Barnum et al. , Phys. Rev. A, 68 (2003) 032308) 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.