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Related Experiment Video

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Quantum walks with quantum chaotic coins: Loschmidt echo, classical limit, and thermalization.

Sivaprasad Omanakuttan¹, Arul Lakshminarayan²

¹Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.

Physical Review. E

|February 19, 2021

Summary

This study explores discrete-time quantum walks using chaotic classical systems as coins. Chaotic coins lead to quantum walks mimicking classical random walkers, showing diffusive and ballistic growth before entanglement saturation.

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Area of Science:

Quantum physics
Classical dynamics
Complex systems

Background:

Discrete-time quantum walks offer a quantum analogue to classical random walks.
Deterministic dynamical systems can serve as 'coins' in quantum walks, introducing classical behavior.
The transition from quantum to classical behavior in such systems is a key research area.

Purpose of the Study:

To investigate discrete-time quantum walks with deterministic dynamical systems as coins.
To analyze the classical limit of these quantum walks, ranging from integrable to chaotic regimes.
To understand the role of quantum entanglement and its saturation in these systems.

Main Methods:

Utilizing deterministic dynamical systems (classical maps) as coins in discrete-time quantum walks.
Employing Loschmidt echo-like fidelity to quantify the quantum-classical correspondence.
Analyzing coin-walker entanglement growth and its dependence on system parameters.

Main Results:

A Loschmidt echo-like fidelity is central to the quantum walk dynamics.
Chaotic coins lead to quantum walks approximating classical random walkers, yielding a binomial distribution.
Quantum walkers exhibit diffusive growth transitioning to ballistic motion.
Coin-walker entanglement grows logarithmically and saturates, depending on relative space dimensions.
Chaos can thermalize the quantum walk to random states in a coin-dominated scenario, saturating entanglement at the Haar-averaged Page value.

Conclusions:

The study demonstrates a clear link between classical chaos in coin dynamics and the emergence of classical random walk behavior.
Entanglement dynamics reveal distinct behaviors in coin-dominated versus walker-dominated regimes, with implications for thermalization and state properties.