Approximate simulation of entanglement with a linear cost of 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.

Added some clarifications. The entanglement model alternative to the Toner-Bacon model is stressed in the abstract and introduction. Added section IIIB

References in corpus (3)

• The Communication Cost of Simulating Bell Correlations
• Measurement contextuality is implied by macroscopic realism
• Compressing the hidden variable space of a qubit

Cited by in corpus (8)

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• Information-based measure of nonlocality
• Exponential communication gap between weak and strong classical simulations of quantum communication
• Generalized Gleason theorem and finite amount of information for the context
• Simulation of Quantum Correlation Functions is not Sufficient Resource to Describe Quantum Entanglement