Related papers: On a time-resolved interpretation of the Husimi fu…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
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…
Gauge-independent Husimi function ($Q-$function) of states of charged quantum particles in the electro-magnetic field is introduced using the gauge-independent Stratonovich-Wigner function, the corresponding dequantizer and quantizer…
This paper presents the measurement problem from the point of view of the thermal interpretation of quantum physics introduced in Part II. The measurement of a Hermitian quantity $A$ is regarded as giving an uncertain value approximating…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this topic is far from being understood. There is no unique way to measure…
We investigate the meaning of the wave function by analyzing the mass and charge density distribution of a quantum system. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus…
Local parametric statistics of zeros of Husimi representations of quantum eigenstates are introduced. It is conjectured that for a classically fully chaotic systems one should use the model of parametric statistics of complex roots of…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalised to…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
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…