2015/03/31 by Marek Mozrzymas, Adam Rutkowski, Michał Studziński · 9 citations
Computer Science · Physics and Astronomy · #Construct (python library) #Generative Adversarial Networks and Image Synthesis #Measure (data warehouse) #Object (grammar) #Observable #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Rank (graph theory) #Set (abstract data type) #Surjective function #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/39/395302
published in Journal of Physics A Mathematical and Theoretical 48(39), 395302 (Institute of Physics) · revised version
openalex publication_date 2015/09/11 · arxiv created 2015/09/24 · arxiv updated 2015/09/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 of rank projectors and the set 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.