  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.
