  In this work we first propose to exploit the fundamental properties of
quantum physics to evaluate the probability of events with projection
measurements. Next, to study what events can be specified by quantum methods,
we introduce the concept of the condition space, which is found to be the dual
space of the classical outcome space of bit strings. Just like the classical
outcome space generates the quantum state space, the condition space generates
the quantum condition space that is the central idea of this work. The quantum
condition space permits the existence of entangled conditions that have no
classical equivalent. In addition, the quantum condition space is related to
the quantum state space by a Fourier transform guaranteed by the Pontryagin
duality, and therefore an entropic uncertainty principle can be defined. The
quantum condition space offers a novel perspective of understanding quantum
states with the duality picture. In addition, the quantum conditions have
physical meanings and realizations of their own and thus may be studied for
purposes beyond the original motivation of characterizing events for
probability evaluation. Finally, the relation between the condition space and
quantum circuits provides insights into how quantum states are collectively
modified by quantum gates, which may lead to deeper understanding of the
complexity of quantum circuits.
