Out-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?

TL;DR

This paper analytically investigates out-of-time-ordered correlators and Loschmidt echo in few-qubit quantum kicked tops, revealing exponential growth signatures even in small systems and exploring quantum-classical correspondence effects.

Contribution

It provides exact analytical solutions for OTOC and Loschmidt echo in 3- and 4-qubit kicked top models, highlighting quantum sensitivity signatures in minimal systems.

Findings

Exponential growth of OTOC observed in systems with as few as 4 qubits.

Classical phase space structures influence quantum measures like OTOC and Loschmidt echo.

A special case shows exponential sensitivity signatures in any number of qubits, bridging quantum and classical behavior.

Abstract

The out-of-time-ordered correlators (OTOC) and the Loschmidt echo are two measures that are now widely being explored to characterize sensitivity to perturbations and information scrambling in complex quantum systems. Studying few qubits systems collectively modelled as a kicked top, we solve exactly the three- and four- qubit cases, giving analytical results for the OTOC and the Loschmidt echo. While we may not expect such few-body systems to display semiclassical features, we find that there are clear signatures of the exponential growth of OTOC even in systems with as low as 4 qubits in appropriate regimes, paving way for possible experimental measurements. We explain qualitatively how classical phase space structures like fixed points and periodic orbits have an influence on these quantities and how our results compare to the large-spin kicked top model. Finally we point to a peculiar case at the border of quantum-classical correspondence which is solvable for any number of qubits and yet has signatures of exponential sensitivity in a rudimentary form.