ire the communication of two classical bits, which is itself limited by the speed of light. We then briefly consider the possibility of denser teleportation schemes, taking, for example, the case of two qubits. Quantum entanglement is also shown to be applicable to the teleportation quantum gates. This opens the perspective of distributed quantum computing: the possibility to manipulate qubits from a distance, or, in a futuristic view, to share the resources of remote quantum networks. Measuring single qubits This section describes the effect of quantum measurements on qubits. We shall first recall some key results obtained in previous chapters, and apply the principles to the case of single qubits and then joint qubit states, including the intriguing case of entan- gled qubits. In Chapter 17, we learnt that given a space of quantum states 1/4/> defined by an orthonormal base V"={|xil}, there exist different possibilities of quantum- measurement operator sets, called {Mm}, corresponding to a number n of possible 18.1 Measuring single qubits measurements indexed by m (m = 1... n). To recall, the two requirements for any such set are (a) that all operator products M+Mm should be positive (which result in the unitarity of M+Mm), and (b) that they satisfy the completeness relation M+Mm = I. The two key results are, first, that the probability of measuring m is given by the bracket: p(m) = (18.1) and, second that the measurement projects the input state into the post-measurement state 1/4') defined as (18.2) Out of many possibilities for any quantum measurement, we can use the measurement in the state basis, where Mm = (xm) (xml is the projector on the pure state /xm). Given the state 1/5/ = it is clear from the definition in Eq. (18.1) with M+Mm = /xm) (xml that the probability that the measurement finds 1/s ) in the state /xm) is p(m) = 1xml2. As we have seen in Chapter 17, the post-measurement state is (18.3) Let the input state be a qubit lq = a|0) + B|1), as defined from the orthonormal base V = {|0), |1)}, and w