Unextendible Maximally Entangled Bases in $\mathbb{C}^{pd}\otimes \mathbb{C}^{qd}$

TL;DR

This paper presents two new methods for constructing unextendible maximally entangled bases in bipartite quantum systems of the form ^{pd}^{qd}, generalizing previous results and providing explicit examples in ^{6}^{9}.

Contribution

The paper introduces two novel constructions of UMEBs in ^{pd}^{qd} systems based on existing UMEBs, extending prior work and offering explicit 48-member examples.

Findings

Two new construction methods for UMEBs in ^{pd}^{qd}.

Explicit 48-member UMEBs in ^{6}^{9}.

Generalization of previous UMEB results.

Abstract

The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in $\mathbb {C}^{pd}\otimes \mathbb {C}^{qd}$($p\leq q$) based on the constructions of UMEBs in $\mathbb {C}^{d}\otimes \mathbb {C}^{d}$ and in $\mathbb {C}^{p}\otimes \mathbb {C}^{q}$, which generalizes the results in [Phys. Rev. A. 94, 052302 (2016)] by two approaches. Two different 48-member UMEBs in $\mathbb {C}^{6}\otimes \mathbb {C}^{9}$ have been constructed in detail.