Measurement induced chaos with entangled states

TL;DR

This paper explores how repeated measurements and entanglement purification protocols induce chaotic behavior in two-qubit systems, revealing sensitivity to initial states, fractal boundaries, and effects of noise.

Contribution

It demonstrates measurement-induced chaos in entangled states and characterizes the asymptotic behavior, including fractal structures and noise effects.

Findings

Measurement-induced non-linear dynamics show chaos and sensitivity to initial conditions.

Distinct asymptotic states include separable and maximally entangled states with fractal boundaries.

Incoherent noise introduces a stable asymptotic cycle.

Abstract

The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. It is shown that the resulting measurement-induced non-linear dynamics of the two-qubit state exhibits strong sensitivity to initial conditions and also true chaos. For a special class of initially prepared two-qubit states two types of islands characterize the asymptotic limit. They correspond to a separable and a maximally entangled two-qubit state, respectively, and their boundaries form fractal-like structures. In the presence of incoherent noise an additional stable asymptotic cycle appears.