483 research outputs found
Gaussian-State Theory of Two-Photon Imaging
Biphoton states of signal and idler fields--obtained from spontaneous
parametric downconversion (SPDC) in the low-brightness, low-flux regime--have
been utilized in several quantum imaging configurations to exceed the
resolution performance of conventional imagers that employ coherent-state or
thermal light. Recent work--using the full Gaussian-state description of
SPDC--has shown that the same resolution performance seen in quantum optical
coherence tomography and the same imaging characteristics found in quantum
ghost imaging can be realized by classical-state imagers that make use of
phase-sensitive cross correlations. This paper extends the Gaussian-state
analysis to two additional biphoton-state quantum imaging scenarios: far field
diffraction-pattern imaging; and broadband thin-lens imaging. It is shown that
the spatial resolution behavior in both cases is controlled by the nonzero
phase-sensitive cross correlation between the signal and idler fields. Thus,
the same resolution can be achieved in these two configurations with
classical-state signal and idler fields possessing a nonzero phase-sensitive
cross correlation.Comment: 14 pages, 5 figure
Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters
Pathwise predictability of continuous time processes is studied in
deterministic setting. We discuss uniform prediction in some weak sense with
respect to certain classes of inputs. More precisely, we study possibility of
approximation of convolution integrals over future time by integrals over past
time. We found that all band-limited processes are predictable in this sense,
as well as high-frequency processes with zero energy at low frequencies. It
follows that a process of mixed type still can be predicted if an ideal
low-pass filter exists for this process.Comment: 10 page
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
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
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
Information rate of waveguide
We calculate the communication capacity of a broadband electromagnetic
waveguide as a function of its spatial dimensions and input power. We analyze
the two cases in which either all the available modes or only a single
directional mode are employed. The results are compared with those for the free
space bosonic channel.Comment: 5 pages, 2 figures. Revised version (minor changes
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]
Persistence of Manifolds in Nonequilibrium Critical Dynamics
We study the persistence P(t) of the magnetization of a d' dimensional
manifold (i.e., the probability that the manifold magnetization does not flip
up to time t, starting from a random initial condition) in a d-dimensional spin
system at its critical point. We show analytically that there are three
distinct late time decay forms for P(t) : exponential, stretched exponential
and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d'
and \eta, z are standard critical exponents. In particular, our theory predicts
that the persistence of a line magnetization decays as a power law in the d=2
Ising model at its critical point. For the d=3 critical Ising model, the
persistence of the plane magnetization decays as a power law, while that of a
line magnetization decays as a stretched exponential. Numerical results are
consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include
Dynamic crossover in the global persistence at criticality
We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure
Fourier Analytic Approach to Phase Estimation
For a unified analysis on the phase estimation, we focus on the limiting
distribution. It is shown that the limiting distribution can be given by the
absolute square of the Fourier transform of function whose support
belongs to . Using this relation, we study the relation between the
variance of the limiting distribution and its tail probability. As our result,
we prove that the protocol minimizing the asymptotic variance does not minimize
the tail probability. Depending on the width of interval, we derive the
estimation protocol minimizing the tail probability out of a given interval.
Such an optimal protocol is given by a prolate spheroidal wave function which
often appears in wavelet or time-limited Fourier analysis. Also, the minimum
confidence interval is derived with the framework of interval estimation that
assures a given confidence coefficient
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