Channel-state duality

Channel-state duality refers to the correspondence between quantum channels and bipartite states, and it is extremely useful and fruitful in quantum information theory. It is often called the Jamiolkowski isomorphism, the Jamiolkowski-Choi isomorphism, or the Choi-Jamiolkowski isomorphism. We trace the original roots of this duality from a historic perspective, clarify the somewhat misleading term isomorphism, reveal the underlying subtle nature, and highlight the seemingly similar but actually different features of the original correspondences in the manner of Pillis, Jamiolkowski, and Choi that lead to the duality. We further illustrate some fundamental properties and diverse applications. DOI: 10.1103/PhysRevA.87.022310