Channel-state duality
Min Jiang, Shunlong Luo, and Shuangshuang Fu
Accepted
The channel-state duality refers to the correspondence between quantum channels and bipartitestates, and is extremely useful and fruitful in quantum information theory. It is often called the Jamiokowski isomorphism, the Jamiokowski-Choi isomorphism, or the Choi-Jamiokowski isomorphism. We trace the original roots of this duality from a historic perspective, clarify the somewhat misleading term of "isomorphism", reveal the underlying subtle nature, highlight the seemingly similar but actually different features, of the original correspondences à la Pillis, Jamiokowski, and Choi, that lead to the duality. We further illustrate some fundamental properties and diverse applications.