The zero-contingent entropic uncertainty relations

This article deals with a new type of uncertainty relation given as the sum of so-called zero-contingent entropies of a pair of observables which do not share any common eigenvector. We show that this uncertainty relation is simpler to handle mathematically than the common entropic uncertainty relation. As examples for demonstrating the difference between the Heisenberg, zero-contingent entropic and common entropic uncertainty relation, we investigate the quantum system with 1/2-spin particle and the finite potential well. We show that, whereas the lower bound of the Heisenberg uncertainty relation for the spin components is zero, the sums of their zero-contingent entropies and information entropies never drop under a certain positive number. Yet, the zero-contingent entropy uncertainty relation is considerably simpler to handle mathematically.