Related papers: Quantum theory without Hilbert spaces
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
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 look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
In this conceptual paper, we discuss quantum formalisms which do not use the famous Axiom of Choice. We also consider the fundamental problem which addresses the (in)correctness of having the complex numbers as the base field for Hilbert…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
The traditional, standard approach to quantum theory is to assume that the theory ``really'' contains only unitary physical dynamics--i.e., that the only physically quantifiable evolution is that given by the time-dependent Schrodinger…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
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…