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

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.

15 pages, 11 Figures

References in corpus (5)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Observation of one-way Einstein-Podolsky-Rosen steering
• Detection Loophole in Bell experiments: How post-selected local correlations can look non-local

Cited by in corpus (4)

• Experimental device-independent verification of quantum steering
• Manipulating the direction of Einstein-Podolsky-Rosen steering
• Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling
• Swapping of Gaussian Einstein-Podolsky-Rosen steering