Efficient classical-communication-assisted local simulation of n-qubit GHZ correlations

Abstract

We present a local hidden-variable model supplemented by classical communication that reproduces the quantum-mechanical predictions for measurements of all products of Pauli operators on an n-qubit GHZ state (or "cat state"). The simulation is efficient since the required amount of communication scales linearly with the number of qubits, even though there are Bell-type inequalities for these states for which the amount of violation grows exponentially with n. The structure of our model yields insight into the Gottesman-Knill theorem by demonstrating that, at least in this limited case, the correlations in the set of nonlocal hidden variables represented by the stabilizer generators are captured by an appropriate set of local hidden variables augmented by n-2 bits of classical communication.