Signatures of Quantum Chaos in an Out-of-Time-Order Tensor.

Area of Science:

• Quantum Information Science
• Quantum Chaos
• Experimental Physics

Background:

• The ink-drop experiment visually demonstrates fluid chaoticity.
• Measuring quantum chaos and scrambling capacity is crucial for quantum information processing.

Purpose of the Study:

• To propose an experimentally implementable method for quantifying the scrambling capacity of quantum processes.
• To introduce a quantum analogue of the out-of-time-order correlator, termed the out-of-time-order tensor.

Main Methods:

• A quantum system of interest interacts with a small quantum probe.
• The dynamical properties of the probe are used to infer the system's chaoticity.
• A novel quantum measure, the out-of-time-order tensor, is developed and analyzed.

Main Results:

• The out-of-time-order tensor provides clear information-theoretic meanings regarding process chaoticity.
• The method is demonstrated using random unitary processes, showcasing its utility as a signature of chaos.
• The quantum kicked rotor model is used to illustrate tunable chaoticity measurement.

Conclusions:

• The proposed out-of-time-order tensor is a viable tool for measuring quantum chaos and scrambling.
• This work offers a practical approach to characterizing complex quantum dynamics.
• The method has implications for understanding and controlling quantum information scrambling.