Related papers: A note on many valued quantum computational logics
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…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
This work uses a simple quantum computer model to discuss the randomness of bit strings originated from integer sequences. The considered quantum computer model has three elements: a processing unit responsible for a mathematical operation,…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
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 notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces.…
We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories…
The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…
The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation)…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…