Classical Cost of Transmitting a Qubit

TL;DR

This paper demonstrates that any prepare-and-measure quantum protocol involving qubits can be perfectly simulated classically with just shared randomness and two bits of communication, establishing this as the minimal classical cost.

Contribution

It proves that two bits of communication suffice and are necessary for simulating quantum correlations in qubit protocols and Bell scenarios.

Findings

Two bits of communication are sufficient for classical simulation.

Two bits of communication are the minimal cost for perfect simulation.

Classical simulation extends to arbitrary local POVMs on entangled two-qubit states.

Abstract

We consider general prepare-and-measure scenarios in which Alice can transmit qubit states to Bob, who can perform general measurements in the form of positive operator-valued measures (POVMs). We show that the statistics obtained in any such quantum protocol can be simulated by the purely classical means of shared randomness and two bits of communication. Furthermore, we prove that two bits of communication is the minimal cost of a perfect classical simulation. In addition, we apply our methods to Bell scenarios, which extends the well-known Toner and Bacon protocol. In particular, two bits of communication are enough to simulate all quantum correlations associated to arbitrary local POVMs applied to any entangled two-qubit state.