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We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a measurement with a given result, which gives the probability distribution for all possible consecutive measurements on the system. This statistical operator, representing the state of the system after the first measurement, is in general not the same that would be obtained using the postulate of collapse.
Considering a minimal number of assumptions and in the context of the timeless formalism, we derive conditional probabilities for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with detection proce
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information such as von Neumann entropy.
We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with repeated strong
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks is learni
Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears when applyi