KINEMATICAL BOUNDS ON EVOLUTION AND OPTIMIZATION OF MIXED QUANTUM STATES

Upper and lower bounds are established for time-dependent ensemble ave rages of observables of driven quantum systems in mixed states. They l imit controllability of observables independently of the control field s. Narrower bounds are established when the observable is a projector onto a pure quantum state or subspace. They are optimal in the sense o f being kinematically achievable. Calculations on nonlinear optimal co ntrol of a four-level model indicate that these kinematical bounds are dynamically achievable asymptotically with increasing control pulse s trength.