

Preprint 65/2013
A note on locally unextendible non-maximally entangled basis
Bin Chen, Halqem Nizamidin, and Shao-Ming Fei
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Submission date: 17. Jul. 2013
Pages: 6
published in: Quantum information and computation, 13 (2013) 11/12, p. 1077-1080
DOI number (of the published article): 10.26421/QIC13.11-12
Bibtex
with the following different title: A note on locally unextendible non-maximally entangled basis : comment on 'Quant. Inf. Comput. 12, 0271(2012)'
Keywords and phrases: Unextendible basis, Non-maximally entangled state
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Abstract:
We study the locally unextendible non-maximally entangled basis
(LUNMEB) in Hd ⊗ Hd. 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.