for the *second* of two measurements. $Q(D)$, on the other hand, is the vector of probabilities associated with a single measurement. Aside from the presence of $\Phi$ matrix, Eq.  is functionally equivalent to the LTP.

Although $P(H)$, $P(D|H)$, and $Q(D)$ are probabilities, $\Phi P(H)$ often is not. One may see by summing both sides of Eq.  over $j$ that the vector is normalized, but in general it may contain negative numbers and values greater than $1$. Such a vector is known as a quasiprobability, and matrices like $\Phi$—real-valued matrices with columns summing to $1$—which take probabilities to quasiprobabilites are called column-quasistochastic matrices [@VanDeWetering:2018]. The subset of column-quasistochastic matrices with nonnegative entries are the column-stochastic matrices. The inverse of a column-stochastic matrix is generally a column-quasistochastic matrix; in our case, inspection of Eq.  reveals that $\Phi^{-1}$ is column-stochastic.

What would it mean if $\Phi$ could equal $I$? In this case we would have $Q(D)=P(D)$. Then, conceptually, it wouldn’t matter if the intermediate measurement were performed or not. Put another way, we could behave as though measurements simply revealed a preexisting property of the system, as in classical physics where measurements provide information about a system’s coordinates in phase space.

Some amount 