Publications
2013
Issue 65

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

65/2013

A note on locally unextendible non-maximally entangled basis

Bin Chen, Halqem Nizamidin and Shao-Ming Fei

Abstract

We study the locally unextendible non-maximally entangled basis (LUNMEB) in $H^{d} ⨂ H^{d}$ . We point out that there exists an error in the proof of the main result of LUNMEB [Quant. Inf. Comput. 12, 0271(2012)], which claims that there are at most $d$ orthogonal vectors in a LUNMEB, constructed from a given non-maximally entangled state. We show that both the proof and the main result are not correct in general. We present a counter example for $d = 4$ , in which five orthogonal vectors from a specific non-maximally entangled state are constructed. Besides, we completely solve the problem of LUNMEB for the case of $d = 2$ .

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Received:: 17.07.13

Published:: 19.07.13

Keywords:: Unextendible basis, Non-maximally entangled state

Related publications

inJournal

2013 Repository Open Access

Bin Chen, Halqem Nizamidin and Shao-Ming Fei

A note on locally unextendible non-maximally entangled basis : comment on 'Quant. Inf. Comput. 12, 0271(2012)'

In: Quantum information and computation, 13 (2013) 11/12, pp. 1077-1080

BibTex DOI: 10.26421/QIC13.11-12 ArXiv: 1304.7412