Eur. Phys. J. D 55, 197-203 (2009)
https://doi.org/10.1140/epjd/e2009-00176-7

Entanglement witnesses and characterizing entanglement properties of some PPT states

¹ Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz, 51664, Iran
² Institute for Studies in Theoretical Physics and Mathematics, Tehran, 19395-1795, Iran
³ Research Institute for Fundamental Sciences, Tabriz, 51664, Iran
⁴ Department of Physics, Azarbaijan University of Tarbiat Moallem, 53714-161, Tabriz, Iran

Corresponding authors: ^a jafarizadeh@tabrizu.ac.ir - ^b behzadi@tabrizu.ac.ir - ^c yakbari@azaruniv.edu

Received: 14 January 2009
Revised: 6 April 2009
Published online: 23 June 2009

Abstract

On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3⊗3 and 4⊗4 systems are constructed. In both cases, the constructed EWs correspond to the hyper-planes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).