14,082 research outputs found
A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
Two quantum information processing protocols are said to be dual under
resource reversal if the resources consumed (generated) in one protocol are
generated (consumed) in the other. Previously known examples include the
duality between entanglement concentration and dilution, and the duality
between coherent versions of teleportation and super-dense coding. A quantum
feedback channel is an isometry from a system belonging to Alice to a system
shared between Alice and Bob. We show that such a resource may be reversibly
decomposed into a perfect quantum channel and pure entanglement, generalizing
both of the above examples. The dual protocols responsible for this
decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum
reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf''
protocol (FQSW), a generalization of the recently discovered ``quantum state
merging'', is related to FF by source-channel duality, and to FQRS by time
reversal duality, thus forming a triangle of dualities. The source-channel
duality is identified as the origin of the previously poorly understood
``mother-father'' duality. Due to a symmetry breaking, the dualities extend
only partially to classical information theory.Comment: 5 pages, 5 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
A General Information Theoretical Proof for the Second Law of Thermodynamics
We show that the conservation and the non-additivity of the information,
together with the additivity of the entropy make the entropy increase in an
isolated system. The collapse of the entangled quantum state offers an example
of the information non-additivity. Nevertheless, the later is also true in
other fields, in which the interaction information is important. Examples are
classical statistical mechanics, social statistics and financial processes. The
second law of thermodynamics is thus proven in its most general form. It is
exactly true, not only in quantum and classical physics but also in other
processes, in which the information is conservative and non-additive.Comment: 4 page
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
Measuring the effective complexity of cosmological models
We introduce a statistical measure of the effective model complexity, called
the Bayesian complexity. We demonstrate that the Bayesian complexity can be
used to assess how many effective parameters a set of data can support and that
it is a useful complement to the model likelihood (the evidence) in model
selection questions. We apply this approach to recent measurements of cosmic
microwave background anisotropies combined with the Hubble Space Telescope
measurement of the Hubble parameter. Using mildly non-informative priors, we
show how the 3-year WMAP data improves on the first-year data by being able to
measure both the spectral index and the reionization epoch at the same time. We
also find that a non-zero curvature is strongly disfavored. We conclude that
although current data could constrain at least seven effective parameters, only
six of them are required in a scheme based on the Lambda-CDM concordance
cosmology.Comment: 9 pages, 4 figures, revised version accepted for publication in PRD,
updated with WMAP3 result
Near-Extreme Black Holes and the Universal Relaxation Bound
A fundamental bound on the relaxation time \tau of a perturbed
thermodynamical system has recently been derived, \tau \geq \hbar/\pi T, where
is the system's temperature. We demonstrate analytically that black holes
saturate this bound in the extremal limit and for large values of the azimuthal
number m of the perturbation field.Comment: 2 Pages. Submitted to PRD on 5/12/200
Lossless quantum data compression and variable-length coding
In order to compress quantum messages without loss of information it is
necessary to allow the length of the encoded messages to vary. We develop a
general framework for variable-length quantum messages in close analogy to the
classical case and show that lossless compression is only possible if the
message to be compressed is known to the sender. The lossless compression of an
ensemble of messages is bounded from below by its von-Neumann entropy. We show
that it is possible to reduce the number of qbits passing through a quantum
channel even below the von-Neumann entropy by adding a classical side-channel.
We give an explicit communication protocol that realizes lossless and
instantaneous quantum data compression and apply it to a simple example. This
protocol can be used for both online quantum communication and storage of
quantum data.Comment: 16 pages, 5 figure
When do generalized entropies apply? How phase space volume determines entropy
We show how the dependence of phase space volume of a classical
system on its size uniquely determines its extensive entropy. We give a
concise criterion when this entropy is not of Boltzmann-Gibbs type but has to
assume a {\em generalized} (non-additive) form. We show that generalized
entropies can only exist when the dynamically (statistically) relevant fraction
of degrees of freedom in the system vanishes in the thermodynamic limit. These
are systems where the bulk of the degrees of freedom is frozen and is
practically statistically inactive. Systems governed by generalized entropies
are therefore systems whose phase space volume effectively collapses to a
lower-dimensional 'surface'. We explicitly illustrate the situation for
binomial processes and argue that generalized entropies could be relevant for
self organized critical systems such as sand piles, for spin systems which form
meta-structures such as vortices, domains, instantons, etc., and for problems
associated with anomalous diffusion.Comment: 5 pages, 2 figure
Information Content of Spontaneous Symmetry Breaking
We propose a measure of order in the context of nonequilibrium field theory
and argue that this measure, which we call relative configurational entropy
(RCE), may be used to quantify the emergence of coherent low-entropy
configurations, such as time-dependent or time-independent topological and
nontopological spatially-extended structures. As an illustration, we
investigate the nonequilibrium dynamics of spontaneous symmetry-breaking in
three spatial dimensions. In particular, we focus on a model where a real
scalar field, prepared initially in a symmetric thermal state, is quenched to a
broken-symmetric state. For a certain range of initial temperatures,
spatially-localized, long-lived structures known as oscillons emerge in
synchrony and remain until the field reaches equilibrium again. We show that
the RCE correlates with the number-density of oscillons, thus offering a
quantitative measure of the emergence of nonperturbative spatiotemporal
patterns that can be generalized to a variety of physical systems.Comment: LaTeX, 9 pages, 5 figures, 1 tabl
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