A note on locally unextendible non-maximally entangled basis

Bin Chen, Halqem Nizamidin, and Shao-Ming Fei

Contact the author: Please use for correspondence this email.
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
Download full preprint: PDF (99 kB)

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.