th the necessary tax of classical information of cbits. As evoked earlier, there exist many sophisticated quantum circuits for the teleportation of single quNits of dimension n, as defined over an orthonormal base V = {|i> by Yn-1/n-1), (18.27) Vi(i=0...n are complex numbers. The first candidate immediately above the qubit is the qutrit = n1|1) + 2212) + 23/3), which is a quantum superposition of the classical trit or three-level information with values 0, 1, 2. Teleporting a single qutrit requires Alice and Bob to share entangled 3-qutrit states, for instance the one defined as 10+) = (|000) + |111) + [222))/3, which is known as a three-level GHZ (Greenberger-Horne-Zeilinger) state (the two-level being the first of the four Bell states, 1Boo)). The extra dimension opens up a large variety of approaches for teleportation algorithms, in particular where a third party, called Charles, comes into the picture! The mediation from Charles simplifies Alice's task in terms of Bell-basis measurements, this time in a 2-qutrit base. These considerations, which are beyond the scope of this book, show at least that, mathematically speaking, teleportation in N dimensions knows no actual limits. Distributed quantum computing The principle of quantum teleportation by means of EPR-Bell states can also be extended to quantum gates. The basic concept is to act on remote qubits from a distance, which is referred to as distributed quantum computation. One way to achieve this would be for Alice and Bob to have their own independent quantum circuits, and use qubit teleportation back and forth to perform computations on each other's qubits. For this, they would use a classical channel to exchange cbits, not only to teleport their qubit data successfully, but also to instruct each other of the computations they want to see the other party performing. For instance, if Alice wants to remotely execute a CNOT operation onto Bob's qubit, Bob needs first to send Alice his qubit, and Alice to send the qubit resulting from her CNOT gate back to 