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Entropy

Construction of a Family of Maximally Entangled Bases in ℂd ⊗ ℂd′

Chenghong Wang, Kun Wang, Zhu‐Jun Zheng

Published Mar 6, 2022• 1 citation
Publisher

Abstract

In this paper, we present a new method for the construction of maximally entangled states in Cd⊗Cd′ when d′≥2d. A systematic way of constructing a set of maximally entangled bases (MEBs) in Cd⊗Cd′ was established. Both cases when d′ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in C2⊗C4, which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in C2⊗C5.

DOI
10.3390/e24030373

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In this paper, we present a new method for the construction of maximally entangled states in Cd⊗Cd′ when d′≥2d. A systematic way of constructing a set of maximally entangled bases (MEBs) in Cd⊗Cd′ was established. Both cases when d′ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in C2⊗C4, which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in C2⊗C5.
We solve the unextendible maximally entangled basis (UMEB) problem in ${\mathbb{C}}^{d}\ensuremath{\bigotimes}{\mathbb{C}}^{{d}^{\ensuremath{'}}}(d\ensuremath{\ne}{d}^{\ensuremath{'}}).$ The results show that a UMEB will always exist. In addition, there might be two sets of UMEBs with different numbers. The main difficulty is to prove the unextendibility of the set of states. We give an explicit construction of UMEBs by considering the Schmidt number of the complementary space of the states we construct.
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