1,538 research outputs found
Phase space measure concentration for an ideal gas
We point out that a special case of an ideal gas exhibits concentration of
the volume of its phase space, which is a sphere, around its equator in the
thermodynamic limit. The rate of approach to the thermodynamic limit is
determined. Our argument relies on the spherical isoperimetric inequality of
L\'{e}vy and Gromov.Comment: 15 pages, No figures, Accepted by Modern Physics Letters
Design optimization of the JPL Phase B testbed
Increasingly complex spacecraft will benefit from integrated design and optimization of structural, optical, and control subsystems. Integrated design optimization will allow designers to make tradeoffs in objectives and constraints across these subsystems. The location, number, and types of passive and active devices distributed along the structure can have a dramatic impact on overall system performance. In addition, the manner in which structural mass is distributed can also serve as an effective mechanism for attenuating disturbance transmission between source and sensitive system components. This paper presents recent experience using optimization tools that have been developed for addressing some of these issues on a challenging testbed design problem. This particular testbed is one of a series of testbeds at the Jet Propulsion Laboratory under the sponsorship of the NASA Control Structure Interaction (CSI) Program to demonstrate nanometer level optical pathlength control on a flexible truss structure that emulates a spaceborne interferometer
Extrapolation theory: new results and applications
AbstractExtending earlier work by Jawerth and Milman, we develop in detail Σ(p) and Δ(p) methods of extrapolation. As an application we prove general forms of Yano's extrapolation theorem. Applications to logarithmic Sobolev inequalities, integrability of maps of finite distortion and logarithmic Sobolev spaces are given
Average output entropy for quantum channels
We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of
quantum channels. This quantity gives information about the average noisiness
of the channel output arising from a typical, highly entangled input state in
the limit of infinite dimensions. We find a closed expression for
\beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We
find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking
channels, and also for the qubit depolarizing channel as a
function of the parameter . We prove equality of the two quantities in
some cases, in particular we conclude that for both are
non-analytic functions of the variable .Comment: 32 pages, several plots and figures; positivity condition added for
Theorem on entanglement breaking channels; new result for entrywise positive
channel
Quantum logic gates using Stark shifted Raman transitions in a cavity
We present a scheme to realise the basic two-quibit logic gates such as
quantum phase gate and controlle-NOT gate using a detuned optical cavity
interacting with a three-level Raman system. We discuss the role of Stark
shifts which are as important as the terms leading to two-photon transition.
The operation of the proposed logic gates involves metastable states of the
atom and hence is not affected by spontaneous emission. These ideas can be
extended to produce multiparticle entanglement.Comment: 5 pages, 1 figure, RevTeX4, Text is modifie
Spacecraft drag-free technology development: On-board estimation and control synthesis
Estimation and control methods for a Drag-Free spacecraft are discussed. The functional and analytical synthesis of on-board estimators and controllers for an integrated attitude and translation control system is represented. The framework for detail definition and design of the baseline drag-free system is created. The techniques for solution of self-gravity and electrostatic charging problems are applicable generally, as is the control system development
Direct measurement of finite-time disentanglement induced by a reservoir
We propose a method for directly probing the dynamics of disentanglement of
an initial two-qubit entangled state, under the action of a reservoir. We show
that it is possible to detect disentanglement, for experimentally realizable
examples of decaying systems, through the measurement of a single observable,
which is invariant throughout the decay. The systems under consideration may
lead to either finite-time or asymptotic disentanglement. A general
prescription for measuring this observable, which yields an operational meaning
to entanglement measures, is proposed, and exemplified for cavity quantum
electrodynamics and trapped ions.Comment: 4 pages, 2 figure
Rate of parity violation from measure concentration
We present a geometric argument determining the kinematic (phase-space)
factor contributing to the relative rate at which degrees of freedom of one
chirality come to dominate over degrees of freedom of opposite chirality, in
models with parity violation. We rely on the measure concentration of a subset
of a Euclidean cube which is controlled by an isoperimetric inequality. We
provide an interpretation of this result in terms of ideas of Statistical
Mechanics.Comment: 10 pages, no figure
Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
We investigate the set a) of positive, trace preserving maps acting on
density matrices of size N, and a sequence of its nested subsets: the sets of
maps which are b) decomposable, c) completely positive, d) extended by identity
impose positive partial transpose and e) are superpositive. Working with the
Hilbert-Schmidt (Euclidean) measure we derive tight explicit two-sided bounds
for the volumes of all five sets. A sample consequence is the fact that, as N
increases, a generic positive map becomes not decomposable and, a fortiori, not
completely positive.
Due to the Jamiolkowski isomorphism, the results obtained for quantum maps
are closely connected to similar relations between the volume of the set of
quantum states and the volumes of its subsets (such as states with positive
partial transpose or separable states) or supersets. Our approach depends on
systematic use of duality to derive quantitative estimates, and on various
tools of classical convexity, high-dimensional probability and geometry of
Banach spaces, some of which are not standard.Comment: 34 pages in Latex including 3 figures in eps, ver 2: minor revision
- …