Related papers: Quantum theory does not need complex numbers
Quantum theory is a well-defined local theory with a clear interpretation. No "measurement problem" or any other foundational matters are waiting to be settled.
Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
The elements of a deterministic quantum theory are developed, which reformulates and extends standard quantum theory. The proposed theory is `realistic' in the sense that in it, a general M-level quantum state is represented by a single…
The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a re-imagining of what fundamental reality, or "ontology", could look like. This thesis…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
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…
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…
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…
Quantum theory is a tremendously successful physical theory, but nevertheless suffers from two serious problems: the measurement problem and the problem of interpretational underdetermination. The latter, however, is largely overlooked as a…
Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that…
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic,…
After more than a century since its birth, Quantum Theory still eludes our understanding. If asked to describe it, we have to resort to abstract and ad hoc principles about complex Hilbert spaces. How is it possible that a fundamental…
This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…
Standard formulations of quantum theory are based on complex numbers: Quantum states can be in superpositions, with weights given by complex probability amplitudes. Motivated by quantum theory promising a range of practical advantages over…