Notation for general quantum teleportation

A new notation for the quantum teleportation of finite dimensional quantum state through a generally entangled quantum channel is introduced. For a given quantum channel an explict mathematical criterion that governs the faithful teleportation is presented. 1 [email protected] Quantum teleportation has been introduced by Benett et al. [1] and discussed by a number of authors for two dimensional quantum state[2][3][4][5]. By means of a classical and distributed quantum communication channel, an unknown quantum state is destroyed at the sending place while its perfect replica state, after some rotation, appears at remote receiving place. Recently, for teleportation of a general finite dimensional quantum state has been discussed in [6] and [7], and the condition of the unitary transformation was given in the[7]. In this letter, we introduced a new notation for quantum teleportation through a generally entangled quantum channel and constructed an explicit nitary transformation U which receiver Bob performed on his qubit. It is adapt to teleport a n-dimensional quantum state by an (n+ 1)-dimension generally entangled channel. At last, we given all the unitary transformation U for the case that both channel and measurement are in the Bell state (maximally entangled state). Let H 1 be the Hilbert space with dimensions N , and {|i〉1 |i = 1...N } be the set of orthogonal basis in H 1. Alice has a general state |φ〉1 unknown to her in the Hilbert space H 1 as, |φ〉 1 = N ∑