Related papers: Emergence of the Partial Trace from Classical Prob…
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…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born's rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative…
A physical experiment comprises along the time trajectory a start, a time evolution (duration), and an end, which is the measurement. In non relativistic quantum mechanics the start of the experiment is defined by the wave function at time…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
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…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
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…
We investigate the equilibration of a small isolated quantum system by means of its matrix of asymptotic transition probabilities in a preferential basis. The trace of this matrix is shown to measure the degree of equilibration of the…
The problem of defining the boundary conditions for the universe is considered here in the framework of a classical dynamical theory, pointing out that a measure on boundary conditions must be included in the theory in order to explain the…
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be…
We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately…