Quantum J-channels on Krein spaces

Abstract

In this paper, we consider Krein spaces and completely J-positive maps between the algebras of bounded linear operators. We first give a Stinespring type representation for a completely J-positive map. We introduce the Choi J-matrix of a linear map and also establish the equivalence of Kraus J-decompositions and Choi J-matrices. We give the J-PPT criterion for separability of J-states and discuss the entanglement breaking condition of quantum J-channels and suggest to prove the J-PPT squared conjecture to solve the PPT squared conjecture. Finally, we gave a concrete example of a completely J-positive map and some examples of 3 circle times 3 quantum J-states which are J-entangled and J-separable.