Measuring higher-dimensional entanglement

TL;DR

This paper demonstrates that a specific Bell-type inequality, the Son-Lee-Kim inequality, can be used to measure entanglement in bipartite qudit states efficiently with only four observables, facilitating experimental implementation.

Contribution

It introduces a novel method to measure entanglement of bipartite qudit states using the Son-Lee-Kim inequality with minimal observables, unlike previous approaches.

Findings

The Son-Lee-Kim inequality can quantify entanglement in pure and certain mixed bipartite qudit states.

The method requires only four observables, independent of system dimension.

Current experimental setups are sufficient to implement this entanglement measurement scheme.

Abstract

We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental set ups can be used to measure the entanglement using our scheme.