Constructions on Real Approximate Mutually Unbiased Bases

TL;DR

This paper introduces a method to construct real approximate mutually unbiased bases (AMUB) in real space from complex AMUB in complex space, resulting in new series with improved parameters for quantum information applications.

Contribution

The paper presents a general method to derive real AMUBs from complex AMUBs, leading to the discovery of many new series with better parameters than previous constructions.

Findings

New series of real AMUBs with improved parameters

Method to derive real AMUBs from complex AMUBs

Enhanced applications in quantum information processing

Abstract

Mutually unbiased bases (MUB) have many applications in quantum information processing and quantum cryptography. Several complex MUB's in $\mathbb{C}^d$ for some dimension $d$ and with larger size have been constructed. On the other hand, real MUB's with larger size are rare which lead to consider constructing approximate MUB (AMUB). In this paper we present a general and useful way to get real AMUB in $\mathbb{R}^{2d}$ from any complex AMUB in $\mathbb{C}^d$. From this method we present many new series of real AMUB's with parameters better than previous results.