Entanglement swapping in critical quantum spin chains

TL;DR

This paper investigates entanglement swapping in critical quantum spin chains using boundary conformal field theory, revealing universal logarithmic scaling of entanglement and verifying results through tensor-network simulations.

Contribution

It introduces a boundary CFT framework to analyze entanglement swapping in critical spin chains, providing universal scaling coefficients and numerical validation.

Findings

Swapped entanglement scales logarithmically with a universal coefficient.

Boundary CFT describes entanglement behavior in critical quantum chains.

Numerical tensor-network calculations confirm theoretical predictions.

Abstract

The transfer of quantum information between many-qubit states is a subject of fundamental importance in quantum science and technology. We consider entanglement swapping in critical quantum spin chains, where the entanglement between the two chains is induced solely by the Bell-state measurements. We employ a boundary conformal field theory (CFT) approach and describe the measurements as conformal boundary conditions in the replicated field theory. We show that the swapped entanglement exhibits a logarithmic scaling, whose coefficient takes a universal value determined by the scaling dimension of the boundary condition changing operator. We apply our framework to the critical spin-1/2 XXZ chain and determine the universal coefficient by the boundary CFT analysis. We also numerically verify these results by the tensor-network calculations. Possible experimental relevance to Rydberg atom arrays is briefly discussed.