Optimal Measurements for Tests of EPR-Steering with No Detection Loophole using Two-Qubit Werner States

TL;DR

This paper develops a method to find optimal measurement strategies for EPR-steering tests with two-qubit Werner states, improving robustness against noise and inefficiency while closing the detection loophole.

Contribution

It introduces a novel optimization approach for designing measurement strategies that are more robust than traditional symmetric measurements in EPR-steering tests.

Findings

Optimal strategies outperform symmetric measurements in robustness

Near-optimal inequalities can be constructed practically for large measurement numbers

Method closes the detection loophole in EPR-steering experiments

Abstract

It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of EPR-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loophole of course), for a given number $n$ of measurement settings. We allow for arbitrary measurement directions, and arbitrary weightings of the outcomes in the EPR-steering inequality. This is a difficult optimization problem for large $n$, so we also consider more practical ways of constructing near-optimal EPR-steering inequalities in this limit.