2012/11/14 by R. Sengupta, Ritabrata Sengupta, Arvind +1
Computer Science · Mathematics · Physics and Astronomy · #Computability, Logic, AI Algorithms #Connection (principal bundle) #Geometry #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #quant-ph
paper · pdf · doi:10.1103/physreva.87.012318
published as Phys. Rev. A 87, 012318 (2013) · 6 pages 2 figures
arxiv created 2012/11/14 · openalex publication_date 2013/01/18 · arxiv updated 2014/08/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we describe a connection between unextendable product bases (UPB) and positive (P) maps which are not completely positive (CP). We show that inner automorphisms of the set of P maps which are not CP produce extremal extensions of these maps that help in entanglement detection. By constructing such an extension of the well-known Choi map, we strengthen its power to unearth positive under partial transpose entangled states. We further show that the class of maps generated from the Choi map via an inner automorphism naturally detects the entanglement of states in the orthogonal complement of certain UPB. This brings out a hitherto undiscovered connection between the Choi map and UPB. We also show that certain other recently considered extremal extensions are obtainable by such extensions of the Choi map.