23,829 research outputs found

### Entanglement and optimal strings of qubits for memory channels

We investigate the problem of enhancement of mutual information by encoding
classical data into entangled input states of arbitrary length and show that
while there is a threshold memory or correlation parameter beyond which
entangled states outperform the separable states, resulting in a higher mutual
information, this memory threshold increases toward unity as the length of the
string increases. These observations imply that encoding classical data into
entangled states may not enhance the classical capacity of quantum channels.Comment: 14 pages, 8 figures, latex, accepted for publication in Physical
Review

### Classical Statistics Inherent in a Quantum Density Matrix

A density matrix formulation of classical bipartite correlations is
constructed. This leads to an understanding of the appearance of classical
statistical correlations intertwined with the quantum correlations as well as a
physical underpinning of these correlations. As a byproduct of this analysis, a
physical basis of the classical statistical correlations leading to additive
entropy in a bipartite system discussed recently by Tsallis et al emerges as
inherent classical spin fluctuations. It is found that in this example, the
quantum correlations shrink the region of additivity in phase space.Comment: 10 pages, 3 figure

### LISA Source Confusion

The Laser Interferometer Space Antenna (LISA) will detect thousands of
gravitational wave sources. Many of these sources will be overlapping in the
sense that their signals will have a non-zero cross-correlation. Such overlaps
lead to source confusion, which adversely affects how well we can extract
information about the individual sources. Here we study how source confusion
impacts parameter estimation for galactic compact binaries, with emphasis on
the effects of the number of overlaping sources, the time of observation, the
gravitational wave frequencies of the sources, and the degree of the signal
correlations. Our main findings are that the parameter resolution decays
exponentially with the number of overlapping sources, and super-exponentially
with the degree of cross-correlation. We also find that an extended mission
lifetime is key to disentangling the source confusion as the parameter
resolution for overlapping sources improves much faster than the usual square
root of the observation time.Comment: 8 pages, 14 figure

### Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information

We show why the amount of information communicated between the past and
future--the excess entropy--is not in general the amount of information stored
in the present--the statistical complexity. This is a puzzle, and a
long-standing one, since the latter is what is required for optimal prediction,
but the former describes observed behavior. We layout a classification scheme
for dynamical systems and stochastic processes that determines when these two
quantities are the same or different. We do this by developing closed-form
expressions for the excess entropy in terms of optimal causal predictors and
retrodictors--the epsilon-machines of computational mechanics. A process's
causal irreversibility and crypticity are key determining properties.Comment: 4 pages, 2 figure

### Configurational entropy of network-forming materials

We present a computationally efficient method to calculate the
configurational entropy of network-forming materials. The method requires only
the atomic coordinates and bonds of a single well-relaxed configuration. This
is in contrast to the multiple simulations that are required for other methods
to determine entropy, such as thermodynamic integration. We use our method to
obtain the configurational entropy of well-relaxed networks of amorphous
silicon and vitreous silica. For these materials we find configurational
entropies of 1.02 kb and 0.97 kb per silicon atom, respectively, with kb the
Boltzmann constant.Comment: 4 pages, 4 figure

### Statistical mechanics of lossy compression using multilayer perceptrons

Statistical mechanics is applied to lossy compression using multilayer
perceptrons for unbiased Boolean messages. We utilize a tree-like committee
machine (committee tree) and tree-like parity machine (parity tree) whose
transfer functions are monotonic. For compression using committee tree, a lower
bound of achievable distortion becomes small as the number of hidden units K
increases. However, it cannot reach the Shannon bound even where K -> infty.
For a compression using a parity tree with K >= 2 hidden units, the rate
distortion function, which is known as the theoretical limit for compression,
is derived where the code length becomes infinity.Comment: 12 pages, 5 figure

### Entanglement can completely defeat quantum noise

We describe two quantum channels that individually cannot send any
information, even classical, without some chance of decoding error. But
together a single use of each channel can send quantum information perfectly
reliably. This proves that the zero-error classical capacity exhibits
superactivation, the extreme form of the superadditivity phenomenon in which
entangled inputs allow communication over zero capacity channels. But our
result is stronger still, as it even allows zero-error quantum communication
when the two channels are combined. Thus our result shows a new remarkable way
in which entanglement across two systems can be used to resist noise, in this
case perfectly. We also show a new form of superactivation by entanglement
shared between sender and receiver.Comment: 4 pages, 1 figur

### The Minimum Description Length Principle and Model Selection in Spectropolarimetry

It is shown that the two-part Minimum Description Length Principle can be
used to discriminate among different models that can explain a given observed
dataset. The description length is chosen to be the sum of the lengths of the
message needed to encode the model plus the message needed to encode the data
when the model is applied to the dataset. It is verified that the proposed
principle can efficiently distinguish the model that correctly fits the
observations while avoiding over-fitting. The capabilities of this criterion
are shown in two simple problems for the analysis of observed
spectropolarimetric signals. The first is the de-noising of observations with
the aid of the PCA technique. The second is the selection of the optimal number
of parameters in LTE inversions. We propose this criterion as a quantitative
approach for distinguising the most plausible model among a set of proposed
models. This quantity is very easy to implement as an additional output on the
existing inversion codes.Comment: Accepted for publication in the Astrophysical Journa

### Information Content of Polarization Measurements

Information entropy is applied to the state of knowledge of reaction
amplitudes in pseudoscalar meson photoproduction, and a scheme is developed
that quantifies the information content of a measured set of polarization
observables. It is shown that this definition of information is a more
practical measure of the quality of a set of measured observables than whether
the combination is a mathematically complete set. It is also shown that when
experimental uncertainty is introduced, complete sets of measurements do not
necessarily remove ambiguities, and that experiments should strive to measure
as many observables as practical in order to extract amplitudes.Comment: 19 pages, 4 figures; figures updated, minor textual correction

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