Induced Entanglement Enhanced by Quantum Criticality

TL;DR

This paper demonstrates that quantum entanglement between two external spins, mediated by a transverse field Ising chain, can be significantly enhanced near the quantum critical point due to the chain's phase transition.

Contribution

It shows how the quantum phase transition of a spin chain can be exploited to enhance induced entanglement between external qubits, using the dynamical structure factor for analysis.

Findings

Entanglement is enhanced near the quantum critical point.

Effective coupling depends on the dynamical structure factor.

Singular behavior observed in the evolution of external spins.

Abstract

Two qubit entanglement can be induced by a quantum data bus interacting with them. In this paper, with the quantum spin chain in the transverse field as an illustration of quantum data bus, we show that such induced entanglement can be enhanced by the quantum phase transition (QPT) of the quantum data bus. We consider two external spins simultaneously coupled to a transverse field Ising chain. By adiabatically eliminating the degrees of the chain, the effective coupling between these two spins are obtained. The matrix elements of the effective Hamiltonian are expressed in terms of dynamical structure factor (DSF) of the chain. The DSF is the Fourier transformation of the Green function of Ising chain and can be calculated numerically by a method introduced in [O. Derzhko, T. Krokhmalskii, Phys. Rev. B \textbf{56}, 11659 (1997)]. Since all characteristics of QPT are embodied in the DSF, the dynamical evolution of the two external spins displays singularity in the vicinity of the critical point.