Entanglement swapping in critical quantum spin chains

We investigate entanglement swapping in critical quantum spin chains, where entanglement between two initially independent chains is induced solely by Bell-state measurements. Using a boundary conformal field theory (CFT) approach, we describe the measurements as conformal boundary conditions in a replicated field theory. We demonstrate that the swapped entanglement exhibits a universal logarithmic scaling with respect to the number of measured qubits. The coefficient of this logarithmic term is determined by the scaling dimension of the boundary condition changing operator.

We apply our framework to the critical spin-1/2 XXZ chain, which is described by the Tomonaga-Luttinger liquid. Through boundary CFT analysis, we determine the universal coefficient to be 1/6. We numerically verify these results using tensor network calculations, confirming the predicted logarithmic scaling and universal coefficient across different anisotropy parameters.

Interestingly, we find that the averaged swapped entanglement, taken over all possible measurement outcomes, also exhibits similar universal behavior. This suggests the emergence of certain conformal boundary conditions in the corresponding replicated field theory.

Our study provides a novel perspective on quantum information transfer in many-body systems and opens up new avenues for exploring the interplay between quantum measurements, criticality, and entanglement in condensed matter physics.