Related papers: Bures Measures over the Spaces of Two and Three-Di…
If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…
In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the…
It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of…
The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements, since it requires a global reconstruction. Here we experimentally demonstrate a scheme that can be used to…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the…
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…
In a number of previous studies, we have investigated the use of the volume element of the Bures (minimal monotone) metric -- identically, one-fourth of the statistical distinguishability (SD) metric -- as a natural measure over the…
Motivated by the existence problem of Fourier frames on fractal measures, we introduce Bessel and frame measures for a given finite measure on $\br^d$, as extensions of the notions of Bessel and frame spectra that correspond to bases of…
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of…
So far, various techniques have been implemented for generating discrete distributions based on continuous distributions. The characteristics and properties of this kind of probability distributions have been studied. Furthermore, the…
We consider the continuous quantum measurement of a two-level system, for example, a single-Cooper-pair box measured by a single-electron transistor or a double-quantum dot measured by a quantum point contact. While the approach most…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention…
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…
We propose a simple and realizable method using a two-particle interferometer for the experimental measurement of pairwise entanglement, assuming some prior knowledge about the quantum state. The basic idea is that the properties of the…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…