Time Optimal Quantum Operartion for Mixed States(Micro-Macro Duality in Quantum Analysis)
A. Carlini, Akio Hosoya, Tatsuhiko Koike, Yosuke Okudaira · Institutional Repositories DataBase (IRDB) · 2007
We formulate a variational principle for finding the time.optimalquantum evolution of mixed states subject to a master equation, when the Hamiltonian $H$ and the Lindblad operators $L_{f}$ are subject to certain constraints.We show that the problem can be reduced to solving first a fun- damental equation (the "quanbum brachistochrone") for $H(t)$ , which can be written down once the $\infty nstraints$ are specified, and then solving the constraints and the master equation for the $L_{f}(t)s$ and the density operator $\rho(t)$ .As an application of our fomalism, we $an\Phi ticM$ solve a simple one $qu$ , bit model where the optimal Lindblad operators correspond either to a measurement or to a decoherence process by the environment.