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
published in: Quantum information and computation, 13 (2013) 11/12, p. 1077-1080
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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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.