Local copying of orthogonal maximally entangled states and its relationship to local discrimination

Abstract

In the quantum system, perfect copying is impossible without prior knowledge. But, perfect copying is possible, if it is known that unknown states to be copied is contained by the set of orthogonal states, which is called the copied set. However, if our operation is limited to local operations and classical communications, this problem is not trivial. Recently, F. Anselmi, A. Chefles and M.B. Plenio constructed theory of local copying when the copied set consists of maximally entangled states. They also classified the copied set when it consists of two orthogonal states (New. J. Phys. 6, 164 (2004)). In this paper, we completely classify the copied set of local copying of the maximally entangled states in the prime dimensional system. That is, we prove that, in the prime dimensional system, the set of locally copiable maximally entangled states is equivalent to the set of Simultaneously Schmidt decomposable canonical form Bell states. As a result, we conclude that local copying of maximally entangled states is much more difficult than local discrimination at least in prime dimensional systems.