Author： Mozrzymas Marek Rutkowski Adam Studziński Michał
Publisher： IOP Publishing
E-ISSN： 1751-8121|48|39|395302-395312
ISSN： 1751-8121
Source： Journal of Physics A: Mathematical and Theoretical, Vol.48, Iss.39, 2015-10, pp. : 395302-395312
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Abstract
In this paper we present a new method for entanglement witnesses construction. We show that to construct such an object we can deal with maps which are not positive on the whole domain, but only on a certain sub-domain. In our approach a crucial role is played by such maps which are surjective between sets &${{mathcal{P}}}_{k}^{d}$; of &$kleqslant d$; rank projectors and the set &${{mathcal{P}}}_{1}^{d}$; of rank one projectors acting in the d dimensional space. We argue that our method can be used to check whether a given observable is an entanglement witness. In the second part of this paper we show that an inverse reduction map satisfies this requirement and using it we can obtain a bunch of new entanglement witnesses.
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