3,878 research outputs found
Digital Signal Processing
Contains reports on one research project.U. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0064)National Science Foundation (Grant GK-31353
Extremal distributions under approximate majorization
Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we consider a notion of approximate majorization. For any distribution, and given a distance δ, we find the approximate distributions which majorize (are majorized by) all other distributions within the distance δ. We call these the steepest and flattest approximation. This enables one to compute how close one can get to a given target distribution under a process governed by majorization. We show that the flattest and steepest approximations preserve ordering under majorization. Furthermore, we give a notion of majorization distance. This has applications ranging from thermodynamics, entanglement theory, and economics
Macroscopically local correlations can violate information causality
Although quantum mechanics is a very successful theory, its foundations are
still a subject of intense debate. One of the main problems is the fact that
quantum mechanics is based on abstract mathematical axioms, rather than on
physical principles. Quantum information theory has recently provided new ideas
from which one could obtain physical axioms constraining the resulting
statistics one can obtain in experiments. Information causality and macroscopic
locality are two principles recently proposed to solve this problem. However
none of them were proven to define the set of correlations one can observe. In
this paper, we present an extension of information causality and study its
consequences. It is shown that the two above-mentioned principles are
inequivalent: if the correlations allowed by nature were the ones satisfying
macroscopic locality, information causality would be violated. This gives more
confidence in information causality as a physical principle defining the
possible correlation allowed by nature.Comment: are welcome. 6 pages, 4 figs. This is the originally submitted
version. The published version contains some bounds on quantum realizations
of d2dd isotropic boxes (table 1), found by T. Vertesi, who kindly shared
them with u
Thermodynamics with long-range interactions: from Ising models to black-holes
New methods are presented which enables one to analyze the thermodynamics of
systems with long-range interactions. Generically, such systems have entropies
which are non-extensive, (do not scale with the size of the system). We show
how to calculate the degree of non-extensivity for such a system. We find that
a system interacting with a heat reservoir is in a probability distribution of
canonical ensembles. The system still possesses a parameter akin to a global
temperature, which is constant throughout the substance. There is also a useful
quantity which acts like a {\it local temperatures} and it varies throughout
the substance. These quantities are closely related to counterparts found in
general relativity. A lattice model with long-range spin-spin coupling is
studied. This is compared with systems such as those encountered in general
relativity, and gravitating systems with Newtonian-type interactions. A
long-range lattice model is presented which can be seen as a black-hole analog.
One finds that the analog's temperature and entropy have many properties which
are found in black-holes. Finally, the entropy scaling behavior of a
gravitating perfect fluid of constant density is calculated. For weak
interactions, the entropy scales like the volume of the system. As the
interactions become stronger, the entropy becomes higher near the surface of
the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22
pages, 2 figure
Discrete-time quadrature feedback cooling of a radio-frequency mechanical resonator
We have employed a feedback cooling scheme, which combines high-frequency
mixing with digital signal processing. The frequency and damping rate of a 2
MHz micromechanical resonator embedded in a dc SQUID are adjusted with the
feedback, and active cooling to a temperature of 14.3 mK is demonstrated. This
technique can be applied to GHz resonators and allows for flexible control
strategies.Comment: To appear in Appl. Phys. Let
Temporal Ordering in Quantum Mechanics
We examine the measurability of the temporal ordering of two events, as well
as event coincidences. In classical mechanics, a measurement of the
order-of-arrival of two particles is shown to be equivalent to a measurement
involving only one particle (in higher dimensions). In quantum mechanics, we
find that diffraction effects introduce a minimum inaccuracy to which the
temporal order-of-arrival can be determined unambiguously. The minimum
inaccuracy of the measurement is given by dt=1/E where E is the total kinetic
energy of the two particles. Similar restrictions apply to the case of
coincidence measurements. We show that these limitations are much weaker than
limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more
accurately than time-of-arrival. To appear in Journal of Physics
Unconditional privacy over channels which cannot convey quantum information
By sending systems in specially prepared quantum states, two parties can
communicate without an eavesdropper being able to listen. The technique, called
quantum cryptography, enables one to verify that the state of the quantum
system has not been tampered with, and thus one can obtain privacy regardless
of the power of the eavesdropper. All previous protocols relied on the ability
to faithfully send quantum states. In fact, until recently, they could all be
reduced to a single protocol where security is ensured though sharing maximally
entangled states. Here we show this need not be the case -- one can obtain
verifiable privacy even through some channels which cannot be used to reliably
send quantum states.Comment: Related to quant-ph/0608195 and for a more general audienc
Short-time homomorphic wavelet estimation
Successful wavelet estimation is an essential step for seismic methods like
impedance inversion, analysis of amplitude variations with offset and full
waveform inversion. Homomorphic deconvolution has long intrigued as a
potentially elegant solution to the wavelet estimation problem. Yet a
successful implementation has proven difficult. Associated disadvantages like
phase unwrapping and restrictions of sparsity in the reflectivity function
limit its application. We explore short-time homomorphic wavelet estimation as
a combination of the classical homomorphic analysis and log-spectral averaging.
The introduced method of log-spectral averaging using a short-term Fourier
transform increases the number of sample points, thus reducing estimation
variances. We apply the developed method on synthetic and real data examples
and demonstrate good performance.Comment: 13 pages, 5 figures. 2012 J. Geophys. Eng. 9 67
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