Ladislav Mista (Department of Optics, Faculty of Sciences, Palacky University)

The talk will focus on building the theoretical foundations of quantum technologies using unorthodox pairs of complementary observables. Instead of the standard position and momentum or spin variables, we will consider angular momentum and the unitary shift operator in the angular momentum of a quantum rotor. The development of the new theory involves proposing a new measure of uncertainty in the angular variable and unifying it with other measures based on an analogy with the moment of inertia, deriving appropriate uncertainty relations, finding the optimal simultaneous measurement of the complementary observables, and establishing the basis for a description of the rotator in phase space. Finally, we also show that the new concepts can be practically used in optimal pulse shaping and detection at the quantum limit.