Local hidden variable models for entangled quantum states using finite shared randomness

TL;DR

This paper demonstrates that most entangled quantum states with local hidden variable models can be simulated using finite shared randomness, reducing the previously assumed need for infinite randomness.

Contribution

It introduces a finite shared randomness model for simulating entangled states, notably Werner states, and discusses extensions to POVMs and nonlocal states.

Findings

Werner states simulated with 3.58 bits of shared randomness

Finite shared randomness suffices for many entangled states

Discussion on simulation of nonlocal states with finite resources

Abstract

The statistics of local measurements performed on certain entangled states can be reproduced using a local hidden variable (LHV) model. While all known models make use of an infinite amount of shared randomness---the physical relevance of which is questionable---we show that essentially all entangled states admitting a LHV model can be simulated with finite shared randomness. Our most economical model simulates noisy two-qubit Werner states using only 3.58 bits of shared randomness. We also discuss the case of POVMs, and the simulation of nonlocal states with finite shared randomness and finite communication. Our work represents a first step towards quantifying the cost of LHV models for entangled quantum states.