1,225 research outputs found
Thermodynamics, stability and Hawking-Page transition of Kerr black holes from R\'enyi statistics
Thermodynamics of rotating black holes described by the R\'enyi formula as
equilibrium and zeroth law compatible entropy function is investigated. We show
that similarly to the standard Boltzmann approach, isolated Kerr black holes
are stable with respect to axisymmetric perturbations in the R\'enyi model. On
the other hand, when the black holes are surrounded by a bath of thermal
radiation, slowly rotating black holes can also be in stable equilibrium with
the heat bath at a fixed temperature, in contrast to the Boltzmann description.
For the question of possible phase transitions in the system, we show that a
Hawking-Page transition and a first order small black hole/large black hole
transition occur, analogous to the picture of rotating black holes in AdS
space. These results confirm the similarity between the R\'enyi-asymptotically
flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating
case as well. We derive the relations between the thermodynamic parameters
based on this correspondence.Comment: 29 pages, 20 figure
Strong converse for the quantum capacity of the erasure channel for almost all codes
A strong converse theorem for channel capacity establishes that the error
probability in any communication scheme for a given channel necessarily tends
to one if the rate of communication exceeds the channel's capacity.
Establishing such a theorem for the quantum capacity of degradable channels has
been an elusive task, with the strongest progress so far being a so-called
"pretty strong converse". In this work, Morgan and Winter proved that the
quantum error of any quantum communication scheme for a given degradable
channel converges to a value larger than in the limit of many
channel uses if the quantum rate of communication exceeds the channel's quantum
capacity. The present paper establishes a theorem that is a counterpart to this
"pretty strong converse". We prove that the large fraction of codes having a
rate exceeding the erasure channel's quantum capacity have a quantum error
tending to one in the limit of many channel uses. Thus, our work adds to the
body of evidence that a fully strong converse theorem should hold for the
quantum capacity of the erasure channel. As a side result, we prove that the
classical capacity of the quantum erasure channel obeys the strong converse
property.Comment: 15 pages, submission to the 9th Conference on the Theory of Quantum
Computation, Communication, and Cryptography (TQC 2014
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Increased markers of cardiac vagal activity in leucine-rich repeat kinase 2-associated Parkinson's disease.
PurposeCardiac autonomic dysfunction manifests as reduced heart rate variability (HRV) in idiopathic Parkinson's disease (PD), but no significant reduction has been found in PD patients who carry the LRRK2 mutation. Novel HRV features have not been investigated in these individuals. We aimed to assess cardiac autonomic modulation through standard and novel approaches to HRV analysis in individuals who carry the LRRK2 G2019S mutation.MethodsShort-term electrocardiograms were recorded in 14 LRRK2-associated PD patients, 25 LRRK2-non-manifesting carriers, 32 related non-carriers, 20 idiopathic PD patients, and 27 healthy controls. HRV measures were compared using regression modeling, controlling for age, sex, mean heart rate, and disease duration. Discriminant analysis highlighted the feature combination that best distinguished LRRK2-associated PD from controls.ResultsBeat-to-beat and global HRV measures were significantly increased in LRRK2-associated PD patients compared with controls (e.g., deceleration capacity of heart rate: p = 0.006) and idiopathic PD patients (e.g., 8th standardized moment of the interbeat interval distribution: p = 0.0003), respectively. LRRK2-associated PD patients also showed significantly increased irregularity of heart rate dynamics, as quantified by Rényi entropy, when compared with controls (p = 0.002) and idiopathic PD patients (p = 0.0004). Ordinal pattern statistics permitted the identification of LRRK2-associated PD individuals with 93% sensitivity and 93% specificity. Consistent results were found in a subgroup of LRRK2-non-manifesting carriers when compared with controls.ConclusionsIncreased beat-to-beat HRV in LRRK2 G2019S mutation carriers compared with controls and idiopathic PD patients may indicate augmented cardiac autonomic cholinergic activity, suggesting early impairment of central vagal feedback loops in LRRK2-associated PD
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
Universal Secure Multiplex Network Coding with Dependent and Non-Uniform Messages
We consider the random linear precoder at the source node as a secure network
coding. We prove that it is strongly secure in the sense of Harada and Yamamoto
and universal secure in the sense of Silva and Kschischang, while allowing
arbitrary small but nonzero mutual information to the eavesdropper. Our
security proof allows statistically dependent and non-uniform multiple secret
messages, while all previous constructions of weakly or strongly secure network
coding assumed independent and uniform messages, which are difficult to be
ensured in practice.Comment: 10 pages, 1 figure, IEEEtrans.cls. Online published in IEEE Trans.
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