Related papers: Quantum measures and integrals
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
Decoherence of a quantum system induced by the interaction with its environment (measuring medium) may be presented phenomenologically as a continuous (or repeated) fuzzy quantum measurement. The dynamics of the system subject to continuous…
The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to…
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…
The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the…
In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
The full anhomomorphic logic of coevents $\ascript ^*$ is introduced. Atoms of $\ascript ^*$ and embeddings of the event set $\ascript$ into $\ascript ^*$ are discussed. The quantum integral over an event $A$ with respect to a coevent…
We discuss various definitions of decoherence and how it can be measured. We compare and contrast decoherence in quantum systems with an infinite number of eigenstates (such as the free particle and the oscillator) and spin systems. In the…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We re-analyse the optomechanical interferometer experiment proposed by Marshall, Simon, Penrose and Bouwmeester with the help of a recently developed quantum-classical hybrid theory. This leads to an alternative evaluation of the mirror…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
Quantum coherence is a key resource in quantum information processing scenarios, and quantifying coherence is an important task for both quantum foundation and quantum technology. However, until now, all most of coherence measures are…
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…
We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the…