11 semigroups”, Comm. Math. Phys. 48 , 119-130 (1976). (2006). [45] J. D. Jackson, Classical Electrodynamics , 3rd Edition, Wiley, New York (1999). [46] L. Boivin, F. X. K¨ artner and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modu- lation with a finite response time”, Phys. Rev. Lett. 73 , 240-243 (1994). [47] For instance, for giant nonlinearities based on EIT we would have Δ vt ≫ w because the light pulses would have a duration in the order of µ s. [41] Strictly speaking, d denotes the initial distance between the pulses inside the medium. [42] Usually the state in which the phase shift is acquired is taken to be | 11 〉 , but we consider | 10 〉 to simplify the discussion. Both gates are related by a single-qubit NOT operation that acts on the second qubit. [43] W. K. Wootters, “Entanglement of Formation of an Ar- bitrary State of Two Qubits”, Phys. Rev. Lett. 80 , 2245- 2248 (1998). [44] G. Lindblad, “On the generators of quantum dynamical