Related papers: Introducing the Qplex: A Novel Arena for Quantum T…
In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…
It has been shown that quantum paradoxes have followed from one special assumption, i.e., from attributing basic physical meaning to Hamiltonian eigenfunctions and representing all physical states by vectors of the Hilbert space spanned on…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
We develop a possibilistic semantic formalism for quantum phenomena from an operational perspective. This semantic system is based on a Chu duality between preparation processes and yes/no tests, the target space being a three-valued set…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
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…
Bell-Kochen-Specker theorem states that a non-contextual hidden-variable theory cannot completely reproduce the predictions of quantum mechanics. Asher Peres gave a remarkably simple proof of quantum contextuality in a four-dimensional…
This is a summary of two lectures I gave at the Davis Conference on Cosmic Inflation. I explain why the quantum theory of de Sitter (dS) space should have a finite number of states and explore gross aspects of the hypothetical quantum…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically…
From the analysis of the measurement process we make the hypothesis that we have to add to the quantum state psi a label z and a special function alpha in order to describe completely the preparation of a (pure) quantum system . Given such…
Combining quantum and Bayesian principles leads to optimality in metrology, but the optimisation equations involved are often hard to solve. This work mitigates this problem with a novel class of measurement strategies for quantities…
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…
An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum…
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state…
The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and…