Related papers: Quantum theory does not need complex numbers

Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be…

Difficulties and discomfort with the interpretation of quantum mechanics are due to differences in language between it and classical physics. Analogies to The Special Theory of Relativity, which also required changes in the basic worldview…

Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is…

An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…

The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…

We are used to the fact that most if not all physical theories are based on the set of real numbers (or another associative division algebra). These all have a cardinality larger than that of the natural numbers, i.e. form a continuum. It…

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…

A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory…

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 theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical…

Despite the unparalleled accuracy of quantum-theoretical predictions across an enormous range of phenomena, the theory's foundations are still in doubt. The theory deviates radically from classical physics, predicts counterintuitive…

Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…

Physicists describe nature using mathematics as the natural language, and for quantum mechanics, it prefers to use complex numbers. However, whether complex numbers are really necessary for the theory has been debated ever since its birth.…

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…

According to Bell's theorem, local realism is incompatible with quantum theory. However, it depends on an implied assumption about quantum measurement. We suggest that the assumption might be removed by a detailed quantum analysis of the…

Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…

Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…

There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications…

Machine learning is frequently listed among the most promising applications for quantum computing. This is in fact a curious choice: Today's machine learning algorithms are notoriously powerful in practice, but remain theoretically…

The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…