A note on the propensity concept in quantum mechanics

Mauricio Suárez

K. Wódkiewicz

In-Rae Cho

Sang-rok Lee

Propensity Theory proposes a foundational root theory encompassing quantum mechanics within a unified deductive framework. Starting from propensity as a fundamental ontological category, the theory explains all phenomena through a five-stage cycle of bond formation and dissolution. Numerical simulations across six quantum phenomena show agreement with established predictions. The theory also introduces Propensity Induction — a methodology for actively designing phenomena. Includes Author's Clarifying Notes on pluralistic realism and the genesis of information.

Piotr Kochański, Krzysztof Wódkiewicz

The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the statistics of the recorded raw data a set of operational quantities that correspond to the intrinsic quantum mechanical observable. Using the concept of the propensity and the associated operational positive operator valued measure (POVM) a general description of the operational algebra of quantum mechanical observables is derived for a wide class of realistic detection schemes. This general approach is illustrated by the example of an operational Malus measurement of the spin phases and by an analysis of the operational homodyne detection of the phase of an optical field with a squeezed vacuum in the unused ports.

Tomáš Opatrný, Vladimír Bužek, J. Bajer +1 more

We present a Q function of a state of a quantum-mechanical system in a finite-dimensional Hilbert space. This discrete Q function is defined with the help of the W\'odkiewicz concept of propensities, i.e., we define the Q function as a discrete convolution of two Wigner functions based on Wootter's formalism, one of the state itself and one of the filter state. The discrete Q function takes nonnegative values in all ``points'' of the discrete phase space and is normalized and it is possible to reconstruct from it the density operator of the state under consideration. We analyze Q-function graphs for several states of interest.