Related papers: A representation of complex rational numbers in qu…
A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place…
A quantum theoretic representation of real and complex numbers is described here as equivalence classes of Cauchy sequences of quantum states of finite strings of qubits. There are 4 types of qubits each with associated single qubit…
Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L…
The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor…
In the presented note we aim at exploring the possibility of abandoning complex numbers in the representation of quantum states and operations. We demonstrate a simplified version of quantum mechanics in which the states are represented…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
In this paper fields of quantum reference frames based on gauge transformations of rational string states are described in a way that, hopefully, makes them more understandable than their description in an earlier paper. The approach taken…
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural…
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables…
A quantum theory representations of real (R) and complex (C) numbers is given that is based on states of single, finite strings of qukits for any base k > 1. Both unary representations and the possibility that qukits with k a prime number…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
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 concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
This paper extends earlier work on quantum theory representations of natural numbers N, integers I, and rational numbers Ra to describe a space of these representations and transformations on the space. The space is parameterized by 4-tuple…
The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with…
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…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
In the Bargmann representation of quantum mechanics, physical states are mapped into entire functions of a complex variable z*, whereas the creation and annihilation operators $\hat{a}^\dagger$ and $\hat{a}$ play the role of multiplication…