Detection efficiency loophole in Pusey-Barrett-Rudolph theorem

TL;DR

This paper analyzes the detection efficiency loophole in the Pusey-Barrett-Rudolph theorem, calculating the critical detection efficiency needed to validate the theorem's implications for quantum state reality.

Contribution

It provides the first calculation of the critical detection efficiency for the PBR theorem in maximally -epistemic models and introduces a method to determine which models are experimentally ruled out.

Findings

Critical detection efficiency threshold identified for PBR theorem validity.

Optimal number of parties for minimal detection efficiency requirement.

A function to determine which epistemic models are incompatible with experimental results.

Abstract

Detection efficiency loophole poses a significant problem for experimental tests of Bell inequalities. Recently discovered Pusey-Barrett-Rudolph (PBR) theorem suffers from the same vulnerability. In this paper we calculate the critical detection efficiency, below which the PBR argument for the ontic nature of quantum state is inconclusive. This is done for the maximally $\psi$-epistemic models. We use two different definitions of this property. The optimal number of parties, for which the critical detection efficiency is the lowest is given. We also approach the problem from the opposite direction. We provide a function which enables us to specify which epistemic models are ruled out by the results of an experiment with a given detection efficiency.