Decoherence of Bell states by local interactions with a dynamic spin environment

TL;DR

This paper provides an exact analysis of how two qubits' entanglement decays due to local interactions with a dynamic spin environment, revealing distance-dependent decoherence and non-Markovian effects.

Contribution

It presents an exact solution for two qubits interacting with a spin chain environment, analyzing decoherence dependence on distance and coupling strength.

Findings

Decoherence increases with distance in the strong coupling regime.

Decoherence depends on initial states in the weak coupling regime.

Evidence of non-Markovian effects causing entanglement revivals.

Abstract

We study the evolution of a system of two qubits, each of which interacts locally with a spin chain with nontrivial internal Hamiltonian. We present an exact solution to this problem and analyze the dependence of decoherence on the distance between the interaction sites. In the strong coupling regime we find that decoherence increases with increasing distance. In the weak coupling regime the dependence of decoherence with distance is not generic (i.e., it varies according to the initial state). Decoherence becomes independent of distance when the latter is over a saturation length $l$. Numerical results for the Ising chain suggest that the saturation scale is related to the correlation length $\xi$. For strong coupling we display evidence of the existence of non--Markovian effects (such as environment--induced interactions between the qubits). As a consequence the system can undergo a quasiperiodic sequence of ``sudden deaths and revivals'' of entanglement, with a time scale related to the distance between qubits.