Relevant out-of-time-order correlator operators: Footprints of the classical dynamics

Area of Science:

• Quantum Information Theory
• Quantum Chaos
• Statistical Mechanics

Background:

• The out-of-time-order correlator (OTOC) is a key observable in quantum information science.
• OTOCs are linked to quantum information scrambling, entanglement, and quantum complexity.
• The OTOC-RE theorem connects summed OTOCs to the second Renyi entropy.

Purpose of the Study:

• To investigate the OTOC-RE correspondence using physically relevant operator bases.
• To explore quantum dynamics and complexity in a bipartite system of perturbed Arnold cat maps.
• To establish a time-dependent complexity measure based on the number of relevant operators.

Main Methods:

• Studied the OTOC-RE correspondence on bases of Pauli, reflection, and translation operators.
• Utilized a bipartite system of two coupled Arnold cat maps with distinct dynamics.
• Analyzed the scaling of relevant operators over time to approximate entropy.

Main Results:

• A small set of relevant operators accurately approximates the second Renyi entropy.
• The scaling of relevant operators with time serves as a natural indicator of quantum complexity.
• Phase space representations of operator sets reveal classical dynamical footprints with varying depth.

Conclusions:

• The OTOC-RE correspondence holds for physically meaningful bases, offering insights into quantum dynamics.
• The number of relevant operators provides an alternative, time-dependent measure of quantum complexity.
• This approach links quantum information scrambling to classical dynamical features in phase space.