Related papers: Conditional expectation and Bayes' rule for quantu…
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In…
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…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
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…
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…