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 ve orthogonal vectors from a specic nonmaximally entangled state are constructed. Besides, we completely solve the problem of LUNMEB for the case of d = 2.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 ve orthogonal vectors from a specic nonmaximally entangled state are constructed. Besides, we completely solve the problem of LUNMEB for the case of d = 2.

Jan 1, 20130 citations

Introduction to Localizable Entanglement

M. Popp, Frank Verstraete, Miguel Angel Martin-Delgado +1 more

Jan 1, 20060 citations

Entanglement Detection by Violations of Noisy Uncertainty Relations: A Proof of Principle

Yuanyuan Zhao, Guo‐Yong Xiang, Xiao‐Min Hu +5 more

It is well known that the violation of a local uncertainty relation can be used as an indicator for the presence of entanglement. Unfortunately, the practical use of these nonlinear witnesses has been limited to few special cases in the past. However, new methods for computing uncertainty bounds have become available. Here we report on an experimental implementation of uncertainty-based entanglement witnesses, benchmarked in a regime dominated by strong local noise. We combine the new computational method with a local noise tomography in order to design noise-adapted entanglement witnesses. This proof-of-principle experiment shows that quantum noise can be successfully handled by a fully quantum model in order to enhance the ability to detect entanglement.It is well known that the violation of a local uncertainty relation can be used as an indicator for the presence of entanglement. Unfortunately, the practical use of these nonlinear witnesses has been limited to few special cases in the past. However, new methods for computing uncertainty bounds have become available. Here we report on an experimental implementation of uncertainty-based entanglement witnesses, benchmarked in a regime dominated by strong local noise. We combine the new computational method with a local noise tomography in order to design noise-adapted entanglement witnesses. This proof-of-principle experiment shows that quantum noise can be successfully handled by a fully quantum model in order to enhance the ability to detect entanglement.

arXiv:1810.05588Physical Review LettersJun 7, 201920 citations

Entanglement and Non-Locality

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more

Springer eBooksJan 1, 200911 citations

A Note on Locally Unextendible Non-Maximally Entangled Basis

Chen, Bin, Halqem Nizamidin, Shao-Ming Fei

We study the locally unextendible non-maximally entangled basis (LUNMEB) in $H^{d}\bigotimes H^{d}$ . 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 $d=2$ .We study the locally unextendible non-maximally entangled basis (LUNMEB) in $H^{d}\bigotimes H^{d}$. 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 $d=2$.

arXiv:1304.7412Apr 28, 20130 citations

We study the locally unextendible non-maximally entangled basis (LUNMEB) in

H^{d}\bigotimes 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