58 research outputs found

### Stationary quantum Markov process for the Wigner function

As a stochastic model for quantum mechanics we present a stationary quantum
Markov process for the time evolution of the Wigner function on a lattice phase
space Z_N x Z_N with N odd. By introducing a phase factor extension to the
phase space, each particle can be treated independently. This is an improvement
on earlier methods that require the whole distribution function to determine
the evolution of a constituent particle. The process has branching and
vanishing points, though a finite time interval can be maintained between the
branchings. The procedure to perform a simulation using the process is
presented.Comment: 12 pages, no figures; replaced with version accepted for publication
in J. Phys. A, title changed, an example adde

### Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

In order to determine the Wigner function uniquely, we introduce a new
condition which ensures that the Wigner function has correct marginal
distributions along tilted lines. For a system in $N$ dimensional Hilbert
space, whose "phase space" is a lattice with $N^2$ sites, we get different
results depending on whether $N$ is odd or even. Under the new condition, the
Wigner function is determined if $N$ is an odd number, but it does not exist if
$N$ is even.Comment: 18 page

### Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually
unbiased bases for a two-qubit system. It is based on an explicit
classification of the geometrical structures compatible with the notion of
unbiasedness. These consist of bundles of discrete curves intersecting only at
the origin and satisfying certain additional properties. We also consider the
feasible transformations between different kinds of curves and show that they
correspond to local rotations around the Bloch-sphere principal axes. We
suggest how to generalize the method to systems in dimensions that are powers
of a prime.Comment: 10 pages. Some typos in the journal version have been correcte

### Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a
preceding paper, we work on the passage from the phase space description of a
degree of freedom described by a finite number of states (without classical
counterpart) to one described by an infinite (and continuously labeled) number
of states. With that it is possible to relate an original Schwinger idea to the
Pegg and Barnett approach to the phase problem. In phase space language, this
discussion shows that one can obtain the Weyl-Wigner formalism, for both
Cartesian {\em and} angular coordinates, as limiting elements of the discrete
phase space formalism.Comment: Subm. to J. Phys A: Math and Gen. 7 pages, sequel of quant-ph/0108031
(which is to appear on J.Phys A: Math and Gen

### Wigner Functions on a Lattice

The Wigner functions on the one dimensional lattice are studied. Contrary to
the previous claim in literature, Wigner functions exist on the lattice with
any number of sites, whether it is even or odd. There are infinitely many
solutions satisfying the conditions which reasonable Wigner functions should
respect. After presenting a heuristic method to obtain Wigner functions, we
give the general form of the solutions. Quantum mechanical expectation values
in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE

### Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations
of infinite-dimensional quantum theory (including the Wigner function) and the
more recently defined quasi-probability representations of finite-dimensional
quantum theory. We focus on both the characteristics and applications of these
representations with an emphasis toward quantum information theory. We discuss
the recently proposed unification of the set of possible quasi-probability
representations via frame theory and then discuss the practical relevance of
negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

### Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects

An approach featuring $s$-parametrized quasiprobability distribution
functions is developed for situations where a circular topology is observed.
For such an approach, a suitable set of angle-angular momentum coherent states
must be constructed in appropriate fashion.Comment: 13 pages, 3 figure

### Framed Hilbert space: hanging the quasi-probability pictures of quantum theory

Building on earlier work, we further develop a formalism based on the
mathematical theory of frames that defines a set of possible phase-space or
quasi-probability representations of finite-dimensional quantum systems. We
prove that an alternate approach to defining a set of quasi-probability
representations, based on a more natural generalization of a classical
representation, is equivalent to our earlier approach based on frames, and
therefore is also subject to our no-go theorem for a non-negative
representation. Furthermore, we clarify the relationship between the
contextuality of quantum theory and the necessity of negativity in
quasi-probability representations and discuss their relevance as criteria for
non-classicality. We also provide a comprehensive overview of known
quasi-probability representations and their expression within the frame
formalism.Comment: 46 pages, 1 table, contains a review of finite dimensional
quasi-probability function

### Social Interactions vs Revisions, What is important for Promotion in Wikipedia?

In epistemic community, people are said to be selected on their knowledge
contribution to the project (articles, codes, etc.) However, the socialization
process is an important factor for inclusion, sustainability as a contributor,
and promotion. Finally, what does matter to be promoted? being a good
contributor? being a good animator? knowing the boss? We explore this question
looking at the process of election for administrator in the English Wikipedia
community. We modeled the candidates according to their revisions and/or social
attributes. These attributes are used to construct a predictive model of
promotion success, based on the candidates's past behavior, computed thanks to
a random forest algorithm.
Our model combining knowledge contribution variables and social networking
variables successfully explain 78% of the results which is better than the
former models. It also helps to refine the criterion for election. If the
number of knowledge contributions is the most important element, social
interactions come close second to explain the election. But being connected
with the future peers (the admins) can make the difference between success and
failure, making this epistemic community a very social community too

### A finite model of two-dimensional ideal hydrodynamics

A finite-dimensional su($N$) Lie algebra equation is discussed that in the
infinite $N$ limit (giving the area preserving diffeomorphism group) tends to
the two-dimensional, inviscid vorticity equation on the torus. The equation is
numerically integrated, for various values of $N$, and the time evolution of an
(interpolated) stream function is compared with that obtained from a simple
mode truncation of the continuum equation. The time averaged vorticity moments
and correlation functions are compared with canonical ensemble averages.Comment: (25 p., 7 figures, not included. MUTP/92/1

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