Approximate simulation of entanglement with a linear cost of communication

TL;DR

This paper introduces three approximate classical protocols with linear communication cost to simulate quantum entanglement, achieving less than 1% error in low dimensions and growing sublinearly with entanglement size.

Contribution

It presents new protocols generalizing existing models for simulating entanglement with linear communication, improving efficiency over previous exponential-cost methods.

Findings

Maximal error less than 1% in three dimensions

Sublinear growth of error with entanglement size

Protocols useful for assessing quantum advantage in communication

Abstract

Bell's theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for n Bell states, but it grows exponentially in n. Three simple protocols are presented that provide approximate simulations for low-dimensional entangled systems and require a linearly growing amount of communication. We have tested them by performing some simulations for a family of measurements. The maximal error is less than 1% in three dimensions and grows sublinearly with the number of entangled bits in the range numerically tested. One protocol is the multidimensional generalization of the exact Toner-Bacon [Phys. Rev. Lett. 91, 187904 (2003)] model for a single Bell state. The other two protocols are generalizations of an alternative exact model, which we derive from the Kochen-Specker [J. Math. Mech. 17, 59 (1967)] scheme for simulating single-qubit measurements. These protocols can give some indication for finding optimal one-way communication protocols that classically simulate entanglement and quantum channels. Furthermore they can be useful for deciding if a quantum communication protocol provides an advantage on classical protocols.