Trap-free manipulation in the Landau-Zener system

The analysis of traps, that is, locally but not globally optimal controls, for quantum control systems has attracted great interest in recent years. The central problem that has remained open is to demonstrate for a given system either the existence or the absence of traps. We prove the absence of traps and hence completely solve this problem for the important tasks of unconstrained manipulation of the transition probability and unitary gate generation in the Landau-Zener system, a system with a wide range of applications across physics, chemistry, and biochemistry. This finding provides an example of a controlled quantum system which is completely free of traps. We also discuss the impact of laboratory constraints due to decoherence, noise in the control pulse, and restrictions on the available controls, which, when being sufficiently severe, can produce traps.