Universal Bell Correlations Do Not Exist

TL;DR

This paper proves that finite-alphabet nonlocal boxes cannot perfectly replicate all correlations from maximally entangled qubits, and such boxes cannot be simulated with finite entanglement if they can simulate all local measurements.

Contribution

It establishes the nonexistence of a universal finite-alphabet nonlocal box for simulating all qubit correlations and provides bounds for approximate simulations.

Findings

No finite-alphabet nonlocal box can generate all maximally entangled qubit correlations.

Finite-alphabet nonlocal boxes capable of simulating all local measurements cannot be simulated with finite entanglement.

Quantitative bounds are provided for approximate simulation capabilities.

Abstract

We prove that there is no finite-alphabet nonlocal box that generates exactly those correlations that can be generated using a maximally entangled pair of qubits. More generally, we prove that if some finite-alphabet nonlocal box is strong enough to simulate arbitrary local projective measurements of a maximally entangled pair of qubits, then that nonlocal box cannot itself be simulated using any finite amount of entanglement. We also give a quantitative version of this theorem for approximate simulations, along with a corresponding upper bound.