Entanglement witnesses from mutually unbiased bases

TL;DR

This paper introduces a new class of entanglement witnesses based on Mutually Unbiased Bases, unifying several known examples and providing a detailed analysis for the three-dimensional case.

Contribution

It presents a novel construction of entanglement witnesses using MUBs, generalizing known maps and analyzing their properties in specific dimensions.

Findings

Reproduces well-known entanglement witnesses like the reduction and Choi maps

Provides a parameterized family of witnesses in 3D based on MUBs

Offers a unified framework for entanglement detection using MUBs

Abstract

We provide a class of entanglement witnesses constructed in terms of Mutually Unbiased Bases (MUBs). This construction reproduces many well-known examples like the celebrated reduction map and Choi map together with its generalizations. We illustrated our construction by the detailed analysis of the 3-dimensional case: in this case, one obtains a family of entanglement witnesses parameterized by an L-dimensional torus (L = 2,3,4 being a number of MUBs used in the construction).