Classical Simulation of Entanglement Swapping with Bounded Communication

Entanglement appears under two different forms in quantum theory, namely, as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We show that even in the more constraining bilocal scenario where distant sources of particles are assumed to be independent, i.e., to share no prior randomness, entanglement swapping can be simulated classically with bounded communication, using only 9 bits in total. Our result thus provides an upper bound on the nonlocality of the entanglement swapping process.

Figure 1

(i) The scenario of entanglement swapping with two fully independent sources of $|{\Psi }_{-}⟩$ states. The Referee sends to Bob the result $r$ of his Bell state measurement. Upon receiving these 2 bits of communication, Bob can apply the adequate unitary operation to his qubit such that Alice and Bob finally share a singlet state. (ii) The classical simulation of entanglement swapping in the bilocal scenario, i.e., with two uncorrelated sources of shared random variables ${\lambda }_{AR}$ and ${\lambda }_{RB}$. The three parties exchange messages symbolized by the thick dashed arrows. Here we present a simulation protocol using 9 bits of communication in total.