Related papers: On classical finite probability theory as a quantu…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
We derive an analogue of the quantum total probability rule by constructing a probability theory based on paraconsistent logic. Bayesian probability theory is constructed upon classical logic and a desiderata, that is, a set of desired…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
We show that classical mechanics can be recovered as the high-entropy limit of quantum mechanics. That is, the high entropy masks quantum effects, and mixed states of high enough entropy can be approximated with classical distributions. The…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…
This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and R\"udiger Schack on the other side. Central to this…
The purpose of the paper is to study the condition for a probability distribution family to a quantum state family. This is an (relatively) easy example of quantum version of "comparison of statistical experiments", which had turned out to…
Modal quantum theory (MQT) is a "toy model" of quantum theory in which amplitudes are elements of a general field. The theory predicts, not the probabilities of a measurement result, but only whether or not a result is possible. In this…
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum…