Related papers: Unifying Aspects of Generalized Calculus
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
In this paper we argue that one-way quantum computation can be seen as a form of phase transition with the available information about the solution of the computation being the order parameter. We draw a number of striking analogies between…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
Quantum information is radically different from classical information in that the quantum formalism (Hilbert space) makes necessary the introduction of irreducible ``nits,'' n being an arbitrary natural number (bigger than one), not just…
The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism. Here we utilize the concepts of identical and similar preparation procedures…
'Tis said, to know others is to be learned, to know oneself, wise - I demonstrate that it could be more fundamental than knowing the rest of nature, by applying classical computational principles and engineering hindsight to derive and…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…