Martin Renner M.Sc., Universität Wien

Martin Renner, M.Sc., Universität Wien

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. In addition, we provide explicit protocols that perfectly simulate the statistics of all local projective measurements on any pair of entangled qubits by communicating one classical trit. If the state is weakly entangled, we prove that a single bit is already sufficient.