Related papers: Quantum scissors - finite-dimensional states engin…
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation, and measurement techniques, in particular, by the…
In the second part of our review (for the first part see quant-ph/0108080), we discuss a physical model for generation of "truncated" coherent and squeezed states in finite-dimensional Hibert spaces.
This article considers quantum systems described by a finite-dimensional complex Hilbert space $H$. We first define the concept of a finite observable on $H$. We then discuss ways of combining observables in terms of convex combinations,…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
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…
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.…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…
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…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
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…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
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 the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…