Related papers: A Representation of Real and Complex Numbers in Qu…
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e.~basis-independent, notion of dimensionality for ensembles of quantum states. It is…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the…
We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science.…
We consider in detail an approach (proposed by the author earlier) where quantum states are described by elements of a linear space over a Galois field, and operators of physical quantities - by linear operators in this space. The notion of…
In this paper, we investigate a characterization of Quantum Mechanics by two physical principles based on general probabilistic theories. We first give the operationally motivated definition of the physical equivalence of states and…
There exist many attempts to define a Wigner function for qudits, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are artificial in their construction and do not allow…
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all…
An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…
In this paper the generalized quantum states, i.e. positive and normalized linear functionals on $C^{*}$-algebras, are studied. Firstly, we study normal states, i.e. states which are represented by density operators, and singular states,…
The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
We introduce the notion of quantum computational webs: These are quantum states universal for measurement-based computation which can be built up from a collection of simple primitives. The primitive elements - reminiscent of building…
We propose a novel method for image representation in quantum computers, which uses the two-dimensional (2-D) quantum states to locate each pixel in an image through row-location and column-location vectors for identifying each pixel…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…