  Just recently, complementarity relations (CRs) have been derived from the
basic rules of Quantum Mechanics. The complete CRs are equalities involving
quantum coherence, $C$, quantum entanglement, and predictability, $P$. While
the first two are already quantified in the resource theory framework, such a
characterization lacks for the last. In this article, we start showing that,
for a system prepared in a state $\rho$, $P$ of $\rho$, with reference to an
observable $X$, is equal to $C$, with reference to observables mutually
unbiased (MU) to $X$, of the state $\Phi_{X}(\rho)$, which is obtained from a
non-revealing von Neumann measurement (NRvNM) of $X$. We also show that
$P^X(\rho)>C^{Y}(\Phi_{X}(\rho))$ for observables not MU. Afterwards, we
provide quantum circuits for implementing NRvNMs and use these circuits to
experimentally test these (in)equalities using the IBM's quantum computers.
Furthermore, we give a resource theory for predictability, identifying its free
quantum states and free quantum operations and discussing some predictability
monotones. Besides, after applying one of these predictability monotones to
study bipartite systems, we discuss the relation among the resource theories of
quantum coherence, predictability, and purity.

Quantum Physics