ENTROPIC UNCERTAINTY RELATIONS FOR OPERATIONAL PHASE-SPACE MEASUREMENT

We introduce entropic measures of uncertainty related to operational p hase-space probability density distributions. With the help of these e ntropies, we find the entropic uncertainty relation for the position ( (q) over cap) and the momentum ((p) over cap) operators of a quantum-m echanical system in the form S-Psi Phi((q)) + S-Psi Phi((p)) greater t han or equal to S-Psi Phi((q,p)) greater than or equal to k(B). The fu ndamental lower bound on the entropic uncertainty relation is equal to the Boltzmann constant k(B).