rce of one shared ebit and two cbits. Various teleportation schemes exist for other gate types, for instance controlled-Z (also called CSIGN for "controlled sign"), which involve somewhat more gate-intensive quantum circuits and ebit resources. 4 Exercises 18.1 (B): Show that there exists no tensor product of single qubits able to generate any of the Bell-EPR states: 18.2 (M): Show that quantum teleportation is possible with EPR-Bell states 1001), 1B10), 1B11). See, for instance: www.iqc.ca/activities/projects/msilva01.php 18.7 Exercises 18.3 (B): Show that a Bell measurement of any of the Bell states 1Bmm') outputs the two classical bits m, m'. (B): Given the EPR-Bell states 1,Boo), 1001), 1810), 1B11) and the Pauli operators X, Y, Z acting on the first qubit, show the following identities used for superdense coding: iY|Boo> = |B11) Z|Boo) = |B10). 18.5 (T): Given the 4-qubit circuit with /Vij) as the input qubit pairs labeled with 1423) = 1Boo) (EPR-Bell state), show that the following equality holds: C34C12(13/14) - x Z'X'C14|1/14) where (i) |0+), 10-),1+), 11-) are tensor products of the |0),|1) states with the |+), 1-) states (| = (|0) + |1))/2); (ii) X, Z are the usual Pauli matrices, used here to the powers 0 or 1, and applying on qubit 1 for Z and qubit 4 for X; (iii) Cij is the CNOT gate for the 2-qubit (Vij), with i as the control qubit and j as the target qubit. Deutsch-Jozsa, quantum Fourier transform, and Grover quantum database search algorithms This mathematically intensive chapter takes us through our first steps in the domain of quantum computation (QC) algorithms. The simplest of them is the Deutsch algorithm, which makes it possible to determine whether or not a Boolean function is constant for any input. The key result is that this QC algorithm provides the answer at once, whereas in the classical case it would take two independent calculations. I describe next the generalization of the former algorithm to n qubits, referred to as the Deutsch-Jozsa algorithm. Although they have no specific or 