Related papers: Physical realization of coupled Hilbert-space mirr…

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our…

We design faster-than-adiabatic state transfers (switching of quantum numbers) in time-dependent coupled-oscillator Hamiltonians. The manipulation to drive the process is found using a two-dimensional invariant recently proposed in S.…

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…

The study of how to generate high-dimensional quantum states (qudits) is justified by the advantages that they can bring for the field of quantum information. However, to have some real practical potential for quantum communication, these…

In this third of a series of four articles, we continue the study of the representations of the hamiltonian dynamical transformations of systems of correlated quantized oscillators. By our use of generalized wave function solutions to…

A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral…

The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…

This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two(many)-particle, `explicitly correlated' basis representation, necessary for…

It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, like the Hamiltonian. Resonances, i.e. states with exponentially decaying observables, are not vectors belonging to the conventional…

We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…

The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…

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…

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…

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…

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…

Pure entangled states of two spatial qudits have been produced by using the momentum transverse correlation of the parametric down-converted photons [Phys. Rev. Lett. \textbf{94} 100501]. Here we show a generalization of this process to…

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization…

We propose a novel setup to investigate the quantum non-locality of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate non-integer spiral phase plates in spatial analyzers, enabling us to use only two…

It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each…

A fundamental goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T2*[1]. Most manipulations of electron spins in quantum dots have focused on the…