Entanglement detection via mutually unbiased bases

TL;DR

This paper presents a method for detecting entanglement in complex quantum systems using mutually unbiased bases, which simplifies experimental procedures and links entanglement detection to the mathematical problem of MUBs.

Contribution

It introduces new entanglement criteria based on MUBs that are practical for high-dimensional and multipartite systems, and connects entanglement detection with the MUBs existence problem.

Findings

Efficient entanglement detection with few measurement settings

Applicable to high-dimensional, multipartite, and continuous variable systems

Links between separability and the maximum number of MUBs

Abstract

We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases (MUBs) for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite and continuous variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases -- opening a new avenue in this long-standing open problem.