相关论文: Quantum States and Complex Projective Space

If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

This work discusses quantum states defined in a finite-dimensional Hilbert space. In particular, after the presentation of some of them and their basic properties the work concentrates on the group of the quantum optical models that can be…

We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…

The notion of entanglement can be naturally extended from quantum-states to the level of general quantum evolutions. This is achieved by considering multi-partite unitary transformations as elements of a multi-partite Hilbert space and then…

We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…

The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An…

It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…

The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…

We consider the quantum dynamical evolution of a fully-connected quantum system subjected to random projective measurements and study the first detection time of an extended subspace of the Hilbert space. Exact analytical expressions are…

This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…

We introduce a class of states of a composite quantum system, the so-called cross states, that turn out to play a major role in the theory of entanglement for a genuinely infinite-dimensional bipartite system. In the case where at least one…

It is obvious that we still have not any unified framework covering a zoo of interpretations of Quantum Mechanics, as well as satisfactory understanding of main ingredients of a phenomena like entanglement. The starting point is an idea to…

We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…

One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…

In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…

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…

This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…