Measurements on quantum chaotic systems

Thomas Dittrich, Robert Graham

Barry C. Sanders, Gerard J Milburn

Jincheng Zhang

This paper proposes a novel approach to quantum measurement based on the principles of chaos theory. It leverages the sensitive dependence on initial conditions inherent in chaotic systems to predict the evolution of quantum states during measurement. The core mechanism involves mapping the quantum measurement process onto a chaotic system, analyzing the resulting probability distributions, and subsequently predicting the outcome of the quantum measurement. This method, termed "pre-reading," aims to anticipate the state of a quantum system before the actual measurement is performed. The theoretical framework presented here offers a fundamentally new perspective on quantum information processing, bridging the gap between deterministic chaos and the probabilistic nature of quantum mechanics. This work explores the potential for enhanced quantum control and information manipulation through the exploitation of chaotic dynamics. We demonstrate a conceptual framework with mathematical formulations outlining the key steps involved in this predictive quantum measurement process.

M. S. Santhanam

Martin Schlautmann, R. Graham

We consider the behavior of a classically chaotic quantum system, the periodically driven pendulum, under the influence of a continuous measurement of its angular momentum. Without measurement the system shows dynamical localization, a quantum interference effect which suppresses the classical chaotic diffusion in momentum space. The coupling of the system to a measuring device destroys its coherence and thus leads to delocalization. This is studied on the level of individual systems including the recording of the measurement results. For that purpose we analyze the appropriate stochastic Schr\"odinger equation, from which a stochastic quantum map is derived as an effective tool for numerical simulation of measurement trajectories. We show that a continuous momentum measurement restores the diffusive behavior of the system in momentum space, but that for sufficiently low accuracy of measurement the corresponding diffusion constant is smaller than the classical one. This is reflected by an equal diffusive growth of the recorded measurement results. Thus we find signatures of the classical chaos and of the dynamical localization both in the behavior of the measured quantum system and in the corresponding signal of the measuring device.

Sarben Sarkar, J.S. Satchell