All teleportation and dense coding schemes (Q2766224)

Consider quantum systems with Hilbert space \(\mathcal H\) of dimension \(d<\infty\). In this paper the equivalence of the following propositions is proved: (1) There are (exact) teleportation schemes. (2) There are (exact) dense coding schemes. (3) There are orthonormal bases of maximally entangled states in \({\mathcal H} \otimes {\mathcal H}\). (4) There are orthonormal bases of unitary operators in \({\mathcal B}({\mathcal H})\) (considered as Schmidt class). (5) There are unitary depolarisers (a certain class of operations defined in the paper). The proof given in the paper is especially instructive since several useful lemmata are formulated and proved. A construction procedure for orthonormal bases of unitary operators is added.