Presentations

We present a general framework for finding the time-optimal quantum evolution of mixed states subject to a master equation, when the Hamiltonian H and the Lindblad operators Lj are subject to certain constraints. The formulation is given by a variational principle and is a generalization of our previous works on pure states. We show in genenal that the problem can be reduced to solving first a fundamental equation (the quantum brachistochrone) for H(t), which can be written down once the constraints are specified, and then solving the constraints and the master equation for the Lj(t)s and the density operator ρ(t). We analytically solve a simple one qubit model where the optimal Lindblad operators correspond either to a measurement or to a decoherence process by the environment.