Unextendible maximally entangled bases and mutually unbiased bases

TL;DR

This paper explores the construction of unextendible maximally entangled bases in bipartite quantum systems and investigates their mutual unbiasedness, providing new examples and methods for such bases.

Contribution

It introduces a systematic construction method for unextendible maximally entangled bases in certain bipartite spaces and studies their mutual unbiasedness.

Findings

Constructed a set of $d^{2}$ orthonormal maximally entangled states in specified bipartite spaces.

Proved the complementary space contains no additional maximally entangled states orthogonal to the set.

Presented two mutually unbiased unextendible maximally entangled bases in $ ext{C}^2 igotimes ext{C}^3$.

Abstract

We study unextendible maximally entangled basis in arbitrary bipartite spaces. A systematic way of constructing a set of $d^{2}$ orthonormal maximally entangled states in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}(\frac{d'}{2}<d<d')$ is provided. The complementary space of the set of these $d^{2}$ orthonormal maximally entangled states contains no maximally entangled states that are orthogonal to all of them. Furthermore, we investigate mutually unbiased bases in which all the bases are unextendible maximally entangled ones. We present two unextendible maximally entangled bases in $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$ which are mutually unbiased.