Communication cost of simulating entanglement swapping

TL;DR

This paper demonstrates that simulating entanglement swapping classically requires infinite communication, highlighting the fundamental nonlocality and complexity of this quantum process.

Contribution

It proves that infinite communication is necessary to classically simulate entanglement swapping in a bilocality scenario, extending previous results on nonlocal correlations.

Findings

Infinite communication needed for simulation

Simulation requires infinite shared randomness or communication

Highlights fundamental nonlocality of entanglement swapping

Abstract

Entanglement appears in two different ways in quantum mechanics, namely as a property of states and as a property of measurement outcomes 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 investigate the communication cost of classically simulating this process. While the communication cost of simulating nonlocal correlations of entangled states appears to be generally quite low, we show here that infinite communication is required to simulate entanglement swapping. This result is derived in the scenario of bilocality, where distant sources of particles are assumed to be independent, and takes advantage of a previous result of Massar et al. [Phys. Rev. A {\bf 63}, 052305 (2001)]. Our result implies that any classical model simulating entanglement swapping must either assume that (i) infinite shared randomness is available between any two locations in the universe, or that (ii) infinite communication takes place.