Discrete Fourier-based Correlations for Entanglement Detection

TL;DR

This paper introduces Fourier-based correlation measures for entanglement detection in qudit systems, providing experimentally feasible methods and bounds for entanglement quantification and inseparability criteria.

Contribution

It presents novel correlation measures based on discrete Fourier transforms for entanglement detection and inseparability in multi-qudit systems, with experimentally accessible measurement schemes.

Findings

Correlation measures can be obtained with two local measurement settings.

Separable bounds are derived from Fourier-based uncertainty relations.

Methods help estimate lower bounds of the Schmidt number.

Abstract

We introduce two forms of correlations on two $d$-level (qudit) systems for entanglement detection. The correlations can be measured via experimentally tractable two local measurement settings and their separable bounds are determined by discrete Fourier-based uncertainty relations. They are useful to estimate lower bounds of the Schmidt number in order to clarify generation of a genuine qudit entanglement. We also present inseparable conditions for multi-qudit systems associated with the qudit stabilizer formalism as another role of the correlations on the inseparability problem.