Classical Cost of Transmitting a Qubit

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.

4 pages main text, 10 pages appendix, matches published version

References in corpus (11)

• The Communication Cost of Simulating Bell Correlations
• Device-independent tests of classical and quantum dimensions
• Semi-device-independent security of one-way quantum key distribution
• Quantum Random Access Codes using Single $d$-level Systems
• Bounding the set of finite dimensional quantum correlations
• Spherical Code Key Distribution Protocols for Qubits
• Classical simulation of entanglement swapping with bounded communication
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol
• Entanglement-assisted quantum communication with simple measurements
• Simulation of bipartite qudit correlations
• Shared randomness and device-independent dimension witnessing

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• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Binarisation of multi-outcome measurements in high-dimensional quantum correlation experiments
• Maximal Elements of Quantum Communication
• Cost of Simulating Entanglement in Steering Scenario
• Beating one bit of communication with and without quantum pseudo-telepathy
• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
• Quantum advantage in a unified scenario and secure detection of resources