Related papers: Probability Distributions and Hilbert Spaces: Quan…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
Transition probabilities for a class of two level systems described by explicitly time dependent Hamiltonians are considered. Provided only that the approach to the infinite time limit is non-trivial falling at least as fast as 1/t for…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
Husimi distributions and Wigner distributions are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of…
We consider ontological models of a quantum system, assuming that not all probability distributions over the space $\Lambda$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a…
This paper extends work done to date on quantum computation by associating potentials with different types of computation steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
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…
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…