230 research outputs found
Operational interpretations of quantum discord
Quantum discord quantifies non-classical correlations going beyond the
standard classification of quantum states into entangled and unentangled ones.
Although it has received considerable attention, it still lacks any precise
interpretation in terms of some protocol in which quantum features are
relevant. Here we give quantum discord its first operational meaning in terms
of entanglement consumption in an extended quantum state merging protocol. We
further relate the asymmetry of quantum discord with the performance imbalance
in quantum state merging and dense coding.Comment: v4: 5 pages, 1 fig. Refs added, text improved. Main results
unchanged. See arXiv:1008.4135v2 for a related work. v5: close to the
published versio
Stochastic growth equations on growing domains
The dynamics of linear stochastic growth equations on growing substrates is
studied. The substrate is assumed to grow in time following the power law
, where the growth index is an arbitrary positive number.
Two different regimes are clearly identified: for small the interface
becomes correlated, and the dynamics is dominated by diffusion; for large
the interface stays uncorrelated, and the dynamics is dominated by
dilution. In this second regime, for short time intervals and spatial scales
the critical exponents corresponding to the non-growing substrate situation are
recovered. For long time differences or large spatial scales the situation is
different. Large spatial scales show the uncorrelated character of the growing
interface. Long time intervals are studied by means of the auto-correlation and
persistence exponents. It becomes apparent that dilution is the mechanism by
which correlations are propagated in this second case.Comment: Published versio
Quantum limits of super-resolution in reconstruction of optical objects
We investigate analytically and numerically the role of quantum fluctuations
in reconstruction of optical objects from diffraction-limited images. Taking as
example of an input object two closely spaced Gaussian peaks we demonstrate
that one can improve the resolution in the reconstructed object over the
classical Rayleigh limit. We show that the ultimate quantum limit of resolution
in such reconstruction procedure is determined not by diffraction but by the
signal-to-noise ratio in the input object. We formulate a quantitative measure
of super-resolution in terms of the optical point-spread function of the
system.Comment: 23 pages, 7 figures. Submitted to Physical Review A e-mail:
[email protected]
Generalized survival in equilibrium step fluctuations
We investigate the dynamics of a generalized survival probability
defined with respect to an arbitrary reference level (rather than the
average) in equilibrium step fluctuations. The exponential decay at large time
scales of the generalized survival probability is numerically analyzed.
is shown to exhibit simple scaling behavior as a function of
system-size , sampling time , and the reference level . The
generalized survival time scale, , associated with is shown
to decay exponentially as a function of .Comment: 4 pages, 2 figure
Slepian functions and their use in signal estimation and spectral analysis
It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden,
Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla
Classical capacity of the lossy bosonic channel: the exact solution
The classical capacity of the lossy bosonic channel is calculated exactly. It
is shown that its Holevo information is not superadditive, and that a
coherent-state encoding achieves capacity. The capacity of far-field,
free-space optical communications is given as an example.Comment: 4 pages, 2 figures (revised version
Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps
We study the geometrical characteristic of quasi-static fractures in
disordered media, using iterated conformal maps to determine the evolution of
the fracture pattern. This method allows an efficient and accurate solution of
the Lam\'e equations without resorting to lattice models. Typical fracture
patterns exhibit increased ramification due to the increase of the stress at
the tips. We find the roughness exponent of the experimentally relevant
backbone of the fracture pattern; it crosses over from about 0.5 for small
scales to about 0.75 for large scales, in excellent agreement with experiments.
We propose that this cross-over reflects the increased ramification of the
fracture pattern.Comment: submitted to Physical Review Letter
Introduction to Random Matrices
These notes provide an introduction to the theory of random matrices. The
central quantity studied is where is the integral
operator with kernel 1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y). Here
and is the characteristic function
of the set . In the Gaussian Unitary Ensemble (GUE) the probability that no
eigenvalues lie in is equal to . Also is a tau-function
and we present a new simplified derivation of the system of nonlinear
completely integrable equations (the 's are the independent variables)
that were first derived by Jimbo, Miwa, M{\^o}ri, and Sato in 1980. In the case
of a single interval these equations are reducible to a Painlev{\'e} V
equation. For large we give an asymptotic formula for , which is
the probability in the GUE that exactly eigenvalues lie in an interval of
length .Comment: 44 page
Scalar and vector Slepian functions, spherical signal estimation and spectral analysis
It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and, particularly for applications in the
geosciences, for scalar and vectorial signals defined on the surface of a unit
sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics,
edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be
published by Springer Verlag. This is a slightly modified but expanded
version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the
Handbook, when it was called: Slepian functions and their use in signal
estimation and spectral analysi
Breakdown of Conformal Invariance at Strongly Random Critical Points
We consider the breakdown of conformal and scale invariance in random systems
with strongly random critical points. Extending previous results on
one-dimensional systems, we provide an example of a three-dimensional system
which has a strongly random critical point. The average correlation functions
of this system demonstrate a breakdown of conformal invariance, while the
typical correlation functions demonstrate a breakdown of scale invariance. The
breakdown of conformal invariance is due to the vanishing of the correlation
functions at the infinite disorder fixed point, causing the critical
correlation functions to be controlled by a dangerously irrelevant operator
describing the approach to the fixed point. We relate the computation of
average correlation functions to a problem of persistence in the RG flow.Comment: 9 page
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