Complex chaos in conditional qubit dynamics and purification protocols

TL;DR

This paper explores how complex chaos arises in the dynamics of quantum state purification, particularly in two-qubit systems, revealing how chaotic oscillations can disrupt the purification process.

Contribution

It extends the study of quantum chaos from single qubits to two-qubit systems, demonstrating how chaos affects purification protocols and the structure of the Julia set.

Findings

Chaotic oscillations can destroy quantum purification in two-qubit systems.

The shape of the Julia set varies with the dynamics parameter.

Complex chaos exhibits true sensitivity to initial conditions.

Abstract

Selection of an ensemble of equally prepared quantum systems, based on measurements on it, is a basic step in quantum state purification. For an ensemble of single qubits, iterative application of selective dynamics has been shown to lead to complex chaos, which is a novel form of quantum chaos with true sensitivity to the initial conditions. The Julia set of initial valuse with no convergence shows a complicated structre on the complex plane. The shape of the Julia set varies with the parameter of the dynamics. We present here results for the two qubit case demonstrating how a purification process can be destroyed with chaotic oscillations.