Related papers: Reformulating and Reconstructing Quantum Theory
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
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…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…
We reconstruct the transformations of quantum theory using a physically motivated postulate. This postulate states that transformations should be locally applicable, and recovers the linear isometries from pure quantum theory, as well as…
Formulations of quantum mechanics can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity…
The standard formalism of quantum mechanics is extended to describe a total system including the reference system (RS), with respect to which the total system is described. The RS is assumed to be able to act as a measuring apparatus, with…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
Any quantum resource theory is based on free states and free operations, i.e., states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
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 physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a…
Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper.…
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to…
We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically…