Locality, detection efficiencies, and probability polytopes

TL;DR

This paper investigates the minimum detection efficiencies required to observe quantum nonlocality in bipartite Bell experiments, using linear programming to analyze the relationship between local and no-signaling probability polytopes.

Contribution

It introduces a method to determine lower bounds on detection efficiencies using polytope analysis, applicable to systems of any dimension and varying input/output configurations.

Findings

Lower bounds depend on the number of inputs and outputs.

Detection efficiencies are constrained by the geometry of probability polytopes.

Numerical results illustrate the efficiency thresholds for different system configurations.

Abstract

We present a detailed investigation of minimum detection efficiencies, below which locality cannot be violated by any quantum system of any dimension in bipartite Bell experiments. Lower bounds on these minimum detection efficiencies are determined with the help of linear programming techniques. Our approach is based on the observation that any possible bipartite quantum correlation originating from a quantum state in an arbitrary dimensional Hilbert space is sandwiched between two probability polytopes, namely the local (Bell) polytope and a corresponding nonlocal no-signaling polytope. Numerical results are presented demonstrating the dependence of these lower bounds on the numbers of inputs and outputs of the bipartite physical system.