High-dimensional entanglement witnessed by correlations in arbitrary bases

TL;DR

This paper extends entanglement certification methods from mutually unbiased bases to arbitrary bases, simplifying high-dimensional entanglement verification across various physical systems and introducing a new three-MUBs construction.

Contribution

It generalizes entanglement certification beyond MUBs to arbitrary bases and proposes a new three-MUBs construction applicable to all dimensions.

Findings

Enables entanglement certification in arbitrary measurement bases.

Introduces a three-MUBs construction for all dimensions.

Facilitates practical high-dimensional entanglement verification.

Abstract

Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key feature distinguishing entanglement from classical correlations is the occurrence of correlations for complementary measurement bases. In particular, mutually unbiased bases (MUBs) are a paradigmatic example that is well-understood and routinely employed for entanglement certification. However, implementing unbiased measurements exactly is challenging and not generically possible for all physical platforms. Here, we extend the entanglement-certification toolbox from correlations in MUBs to arbitrary bases. This practically significant simplification paves the way for efficient characterizations of high-dimensional entanglement in a wide range of physical systems. Furthermore, we introduce a simple three-MUBs construction for all dimensions without using the Wootters-Fields construction, potentially simplifying experimental requirements when measurements in more than two MUBs are needed, especially in high-dimensional settings.