Constructions of Unextendible Maximally Entangled Bases in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\)

Abstract

We study unextendible maximally entangled bases (UMEBs) in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d^{\prime }$). An operational method to construct UMEBs containing $d(d^{\prime }-1)$ maximally entangled vectors is established, and two UMEBs in \(\mathbb {C}^{5}\otimes \mathbb {C}^{6}\) and \(\mathbb {C}^{5}\otimes \mathbb {C}^{12}\) are given as examples. Furthermore, a systematic way of constructing UMEBs containing $d(d^{\prime }-r)$ maximally entangled vectors in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) is presented for $r=1,2,\cdots ,d-1$. Correspondingly, two UMEBs in \(\mathbb {C}^{3}\otimes \mathbb {C}^{10}\) are obtained.

arXiv comment8 pages

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Cited by in corpus (5)

• Separability and entanglement in superpositions of quantum states
• Unextendible entangled bases and more nonlocality with less entanglement
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
• Constructing mutually unbiased bases from unextendible maximally entangled bases
• An extension of Bravyi-Smolin's construction for UMEBs