We formulate a variational principle for finding the time-optimal quantum evolution of mixed states governed by the master equation, when the Hamiltonian H and the Lindblad operators Lj are subject to certain constraints. We show 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). As an application of our formalism, we analytically solve a simple one qubit model where the optimal Lindblad operators correspond either to a continuous Markovian measurement or to a decoherence process by the environment.
|Title of host publication||Quantum Bio-informatics|
|Subtitle of host publication||From Quantum Information To Bio-informatics|
|Publisher||World Scientific Publishing Co.|
|Number of pages||11|
|Publication status||Published - 2008 Jan 1|
ASJC Scopus subject areas
- Physics and Astronomy(all)