Related papers: Tagged vector space, Part II: function space index…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in…
A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…
We outline the rationale and preliminary results of using the state context property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used and…
The geometric construction of the functional integral over coset spaces ${\cal M}/{\cal G}$ is reviewed. The inner product on the cotangent space of infinitesimal deformations of $\cal M$ defines an invariant distance and volume form, or…
This paper aims to give a probabilistic construction of interactions which may be relevant for building physical theories such as interacting quantum field theories. We start with the path integral definition of partition function in…
We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family,…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
We show that conditional output measurement on a beam splitter may be used to produce photon-added states for a large class of signal-mode quantum states, such as thermal states, coherent states, squeezed states, displaced photon-number…
The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…
The splitting of the tangent bundle of space-time into temporal and spatial sub-bundles defines an almost-product structure. In particular, any space-time metric can be locally expressed in time-orthogonal form, in such a way that whether…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
Schwinger's algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, was presented in two previous…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with…
In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…
We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference…
According to Hudson's theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step towards the extension of this theorem to mixed quantum states by finding upper and lower bounds on…