15,990 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
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
Quantum Entanglement Capacity with Classical Feedback
For any quantum discrete memoryless channel, we define a quantity called
quantum entanglement capacity with classical feedback (), and we show that
this quantity lies between two other well-studied quantities. These two
quantities - namely the quantum capacity assisted by two-way classical
communication () and the quantum capacity with classical feedback ()
- are widely conjectured to be different: there exists quantum discrete
memoryless channel for which . We then present a general scheme to
convert any quantum error-correcting codes into adaptive protocols for this
newly-defined quantity of the quantum depolarizing channel, and illustrate with
Cat (repetition) code and Shor code. We contrast the present notion with
entanglement purification protocols by showing that whilst the Leung-Shor
protocol can be applied directly, recurrence methods need to be supplemented
with other techniques but at the same time offer a way to improve the
aforementioned Cat code. For the quantum depolarizing channel, we prove a
formula that gives lower bounds on the quantum capacity with classical feedback
from any protocols. We then apply this formula to the protocols
that we discuss to obtain new lower bounds on the quantum capacity with
classical feedback of the quantum depolarizing channel
Entropy exchange and entanglement in the Jaynes-Cummings model
The Jaynes-Cummings model is the simplest fully quantum model that describes
the interaction between light and matter. We extend a previous analysis by
Phoenix and Knight (S. J. D. Phoenix, P. L. Knight, Annals of Physics 186,
381). of the JCM by considering mixed states of both the light and matter. We
present examples of qualitatively different entropic correlations. In
particular, we explore the regime of entropy exchange between light and matter,
i.e. where the rate of change of the two are anti-correlated. This behavior
contrasts with the case of pure light-matter states in which the rate of change
of the two entropies are positively correlated and in fact identical. We give
an analytical derivation of the anti-correlation phenomenon and discuss the
regime of its validity. Finally, we show a strong correlation between the
region of the Bloch sphere characterized by entropy exchange and that
characterized by minimal entanglement as measured by the negative eigenvalues
of the partially transposed density matrix.Comment: 8 pages, 5 figure
The most probable wave function of a single free moving particle
We develop the most probable wave functions for a single free quantum
particle given its momentum and energy by imposing its quantum probability
density to maximize Shannon information entropy. We show that there is a class
of solutions in which the quantum probability density is self-trapped with
finite-size spatial support, uniformly moving hence keeping its form unchanged.Comment: revtex, 4 page
Incomplete quantum process tomography and principle of maximal entropy
The main goal of this paper is to extend and apply the principle of maximum
entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define
a so-called process entropy function being the von Neumann entropy of the state
associated with the quantum process via Choi-Jamiolkowski isomorphism. It will
be shown that an arbitrary process estimation experiment can be reformulated in
a unified framework and MaxEnt principle can be consistently exploited. We will
argue that the suggested choice for the process entropy satisfies natural list
of properties and it reduces to the state MaxEnt principle, if applied to
preparator devices.Comment: 8 pages, comments welcome, references adde
Maximum Path Information and Fokker-Planck Equation
We present in this paper a rigorous method to derive the nonlinear
Fokker-Planck (FP) equation of anomalous diffusion directly from a
generalization of the principle of least action of Maupertuis proposed by Wang
for smooth or quasi-smooth irregular dynamics evolving in Markovian process.
The FP equation obtained may take two different but equivalent forms. It was
also found that the diffusion constant may depend on both q (the index of
Tsallis entropy) and the time t.Comment: 7 page
Abstract composition rule for relativistic kinetic energy in the thermodynamical limit
We demonstrate by simple mathematical considerations that a power-law tailed
distribution in the kinetic energy of relativistic particles can be a limiting
distribution seen in relativistic heavy ion experiments. We prove that the
infinite repetition of an arbitrary composition rule on an infinitesimal amount
leads to a rule with a formal logarithm. As a consequence the stationary
distribution of energy in the thermodynamical limit follows the composed
function of the Boltzmann-Gibbs exponential with this formal logarithm. In
particular, interactions described as solely functions of the relative
four-momentum squared lead to kinetic energy distributions of the
Tsallis-Pareto (cut power-law) form in the high energy limit.Comment: Submitted to Europhysics Letters. LaTeX, 3 eps 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 preserving structures: A general framework for quantum zero-error information
Quantum systems carry information. Quantum theory supports at least two
distinct kinds of information (classical and quantum), and a variety of
different ways to encode and preserve information in physical systems. A
system's ability to carry information is constrained and defined by the noise
in its dynamics. This paper introduces an operational framework, using
information-preserving structures to classify all the kinds of information that
can be perfectly (i.e., with zero error) preserved by quantum dynamics. We
prove that every perfectly preserved code has the same structure as a matrix
algebra, and that preserved information can always be corrected. We also
classify distinct operational criteria for preservation (e.g., "noiseless",
"unitarily correctible", etc.) and introduce two new and natural criteria for
measurement-stabilized and unconditionally preserved codes. Finally, for
several of these operational critera, we present efficient (polynomial in the
state-space dimension) algorithms to find all of a channel's
information-preserving structures.Comment: 29 pages, 19 examples. Contains complete proofs for all the theorems
in arXiv:0705.428
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