3,761 research outputs found
Nonuniform Fuchsian codes for noisy channels
We develop a new transmission scheme for additive white Gaussian noisy (AWGN)
channels based on Fuchsian groups from rational quaternion algebras. The
structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence
conventional decoding methods based on linearity and symmetry do not apply.
Previously, only brute force decoding methods with complexity that is linear in
the code size exist for general nonuniform codes. However, the properly
discontinuous character of the action of the Fuchsian groups on the complex
upper half-plane translates into decoding complexity that is logarithmic in the
code size via a recently introduced point reduction algorithm
Higher-U(2,2)-spin fields and higher-dimensional W-gravities: quantum AdS space and radiation phenomena
A physical and geometrical interpretation of previously introduced tensor
operator algebras of U(2,2) in terms of algebras of higher-conformal-spin
quantum fields on the anti-de Sitter space AdS_5 is provided. These are
higher-dimensional W-like algebras and constitute a potential gauge guide
principle towards the formulation of induced conformal gravities
(Wess-Zumino-Witten-like models) in realistic dimensions. Some remarks on
quantum (Moyal) deformations are given and potentially tractable versions of
noncommutative AdS spaces are also sketched. The role of conformal symmetry in
the microscopic description of Unruh and Hawking's radiation effects is
discussed.Comment: LaTeX, 30 pages, 2 figures, final version to appear in Class. and
Quant. Gra
Flux Analysis in Process Models via Causality
We present an approach for flux analysis in process algebra models of
biological systems. We perceive flux as the flow of resources in stochastic
simulations. We resort to an established correspondence between event
structures, a broadly recognised model of concurrency, and state transitions of
process models, seen as Petri nets. We show that we can this way extract the
causal resource dependencies in simulations between individual state
transitions as partial orders of events. We propose transformations on the
partial orders that provide means for further analysis, and introduce a
software tool, which implements these ideas. By means of an example of a
published model of the Rho GTP-binding proteins, we argue that this approach
can provide the substitute for flux analysis techniques on ordinary
differential equation models within the stochastic setting of process algebras
Distillability and positivity of partial transposes in general quantum field systems
Criteria for distillability, and the property of having a positive partial
transpose, are introduced for states of general bipartite quantum systems. The
framework is sufficiently general to include systems with an infinite number of
degrees of freedom, including quantum fields. We show that a large number of
states in relativistic quantum field theory, including the vacuum state and
thermal equilibrium states, are distillable over subsystems separated by
arbitrary spacelike distances. These results apply to any quantum field model.
It will also be shown that these results can be generalized to quantum fields
in curved spacetime, leading to the conclusion that there is a large number of
quantum field states which are distillable over subsystems separated by an
event horizon.Comment: 25 pages, 2 figures. v2: Typos removed, references and comments
added. v3: Expanded introduction and reference list. To appear in Rev. Math.
Phy
Group transference techniques for the estimation of the decoherence times and capacities of quantum Markov semigroups
Capacities of quantum channels and decoherence times both quantify the extent
to which quantum information can withstand degradation by interactions with its
environment. However, calculating capacities directly is known to be
intractable in general. Much recent work has focused on upper bounding certain
capacities in terms of more tractable quantities such as specific norms from
operator theory. In the meantime, there has also been substantial recent
progress on estimating decoherence times with techniques from analysis and
geometry, even though many hard questions remain open. In this article, we
introduce a class of continuous-time quantum channels that we called
transferred channels, which are built through representation theory from a
classical Markov kernel defined on a compact group. We study two subclasses of
such kernels: H\"ormander systems on compact Lie-groups and Markov chains on
finite groups. Examples of transferred channels include the depolarizing
channel, the dephasing channel, and collective decoherence channels acting on
qubits. Some of the estimates presented are new, such as those for channels
that randomly swap subsystems. We then extend tools developed in earlier work
by Gao, Junge and LaRacuente to transfer estimates of the classical Markov
kernel to the transferred channels and study in this way different
non-commutative functional inequalities. The main contribution of this article
is the application of this transference principle to the estimation of various
capacities as well as estimation of entanglement breaking times, defined as the
first time for which the channel becomes entanglement breaking. Moreover, our
estimates hold for non-ergodic channels such as the collective decoherence
channels, an important scenario that has been overlooked so far because of a
lack of techniques.Comment: 35 pages, 2 figures. Close to published versio
Languages of Quantum Information Theory
This note will introduce some notation and definitions for information
theoretic quantities in the context of quantum systems, such as (conditional)
entropy and (conditional) mutual information. We will employ the natural
C*-algebra formalism, and it turns out that one has an allover dualism of
language: we can define everything for (compatible) observables, but also for
(compatible) C*-subalgebras. The two approaches are unified in the formalism of
quantum operations, and they are connected by a very satisfying inequality,
generalizing the well known Holevo bound. Then we turn to communication via
(discrete memoryless) quantum channels: we formulate the Fano inequality, bound
the capacity region of quantum multiway channels, and comment on the quantum
broadcast channel.Comment: 16 pages, REVTEX, typos corrected, references added and extende
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