1,124 research outputs found
Improving Detectors Using Entangling Quantum Copiers
We present a detection scheme which using imperfect detectors, and imperfect
quantum copying machines (which entangle the copies), allows one to extract
more information from an incoming signal, than with the imperfect detectors
alone.Comment: 4 pages, 2 figures, REVTeX, to be published in Phys. Rev.
Stably reflexive modules and a lemma of Knudsen
In his fundamental work on the stack of stable n-pointed genus g curves, Finn
F. Knudsen introduced the concept of a stably reflexive module in order to
prove a key technical lemma. We propose an alternative definition and
generalise the results in the appendix to his article. Then we give a
`coordinate free' generalisation of his lemma, generalise a construction used
in Knudsen's proof concerning versal families of pointed algebras, and show
that Knudsen's stabilisation construction works for plane curve singularities.
In addition we prove approximation theorems generalising Cohen-Macaulay
approximation with stably reflexive modules in flat families. The
generalisation is not covered (even in the closed fibres) by the
Auslander-Buchweitz axioms.Comment: 27 pages. The statement in Thm. 6.1 (iv) has been corrected. Many
proofs have been expanded. A few minor changes in some of the statements.
Comments and an example added. To appear in J. Algebr
Equivalent efficiency of a simulated photon-number detector
Homodyne detection is considered as a way to improve the efficiency of
communication near the single-photon level. The current lack of commercially
available {\it infrared} photon-number detectors significantly reduces the
mutual information accessible in such a communication channel. We consider
simulating direct detection via homodyne detection. We find that our particular
simulated direct detection strategy could provide limited improvement in the
classical information transfer. However, we argue that homodyne detectors (and
a polynomial number of linear optical elements) cannot simulate photocounters
arbitrarily well, since otherwise the exponential gap between quantum and
classical computers would vanish.Comment: 4 pages, 4 figure
Critical Noise Levels for LDPC decoding
We determine the critical noise level for decoding low density parity check
error correcting codes based on the magnetization enumerator (\cM), rather
than on the weight enumerator (\cW) employed in the information theory
literature. The interpretation of our method is appealingly simple, and the
relation between the different decoding schemes such as typical pairs decoding,
MAP, and finite temperature decoding (MPM) becomes clear. In addition, our
analysis provides an explanation for the difference in performance between MN
and Gallager codes. Our results are more optimistic than those derived via the
methods of information theory and are in excellent agreement with recent
results from another statistical physics approach.Comment: 9 pages, 5 figure
Quantum Stabilizer Codes and Classical Linear Codes
We show that within any quantum stabilizer code there lurks a classical
binary linear code with similar error-correcting capabilities, thereby
demonstrating new connections between quantum codes and classical codes. Using
this result -- which applies to degenerate as well as nondegenerate codes --
previously established necessary conditions for classical linear codes can be
easily translated into necessary conditions for quantum stabilizer codes.
Examples of specific consequences are: for a quantum channel subject to a
delta-fraction of errors, the best asymptotic capacity attainable by any
stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the
depolarizing channel with fidelity parameter delta, the best asymptotic
capacity attainable by any stabilizer code cannot exceed 1-H(delta).Comment: 17 pages, ReVTeX, with two figure
Statistical mechanics of lossy data compression using a non-monotonic perceptron
The performance of a lossy data compression scheme for uniformly biased
Boolean messages is investigated via methods of statistical mechanics. Inspired
by a formal similarity to the storage capacity problem in the research of
neural networks, we utilize a perceptron of which the transfer function is
appropriately designed in order to compress and decode the messages. Employing
the replica method, we analytically show that our scheme can achieve the
optimal performance known in the framework of lossy compression in most cases
when the code length becomes infinity. The validity of the obtained results is
numerically confirmed.Comment: 9 pages, 5 figures, Physical Review
Thouless-Anderson-Palmer Approach for Lossy Compression
We study an ill-posed linear inverse problem, where a binary sequence will be
reproduced using a sparce matrix. According to the previous study, this model
can theoretically provide an optimal compression scheme for an arbitrary
distortion level, though the encoding procedure remains an NP-complete problem.
In this paper, we focus on the consistency condition for a dynamics model of
Markov-type to derive an iterative algorithm, following the steps of
Thouless-Anderson-Palmer's. Numerical results show that the algorithm can
empirically saturate the theoretical limit for the sparse construction of our
codes, which also is very close to the rate-distortion function.Comment: 10 pages, 3 figure
Skeletal muscle carnitine metabolism during intense exercise in human volunteers
Increasing skeletal muscle carnitine content enhances PDC flux during 30 minutes of continuous exercise at 80% Wmax, reducing reliance on non-mitochondrial ATP production and improving work output. These studies in healthy volunteers evaluated a carnitine feeding strategy that did not rely on the high carbohydrate load previously used, then investigated whether manipulating muscle carnitine could alter the adaptations to a period of submaximal high-intensity intermittent training (HIT).
The rate of orally ingested 2H3-carnitine uptake into skeletal muscle was directly quantified for the first time in vivo and increased 5-fold following ingestion of an 80g carbohydrate formulation. This positive forearm carnitine balance was entirely blunted when the carbohydrate load was supplemented with 40g of whey protein, suggesting a novel antagonisation of insulin-stimulated muscle carnitine transport by amino acids.
Skeletal muscle biopsy sampling demonstrated minimal acetylcarnitine accumulation and non-mitochondrial ATP production during single-leg knee extension at 85% Wmax, suggesting that PDC flux does not limit oxidative ATP production under these conditions. Conversely, PDC flux declined over repeated bouts of cycling at 100% Wmax, as evidenced by greater non-mitochondrial ATP production in the face of similar acetylcarnitine accumulation. This suggested that muscle carnitine availability could influence oxidative ATP delivery during submaximal HIT.
Manipulation of muscle carnitine content by daily carnitine/carbohydrate feeding elevated free carnitine availability and maintained PDC flux during repeated bouts of intense exercise. However, profound improvements in oxidative ATP delivery in response to HIT eclipsed any effect of this carnitine-mediated increase in PDC flux on non-mitochondrial ATP production and indeed, carnitine supplementation did not potentiate any increases in exercise capacity above submaximal HIT alone.
These novel data advance our understanding of muscle carnitine transport and the interplay between carnitine metabolism, PDC flux and non-mitochondrial ATP production during intense exercise, having important implications for the development of nutritional and exercise prescription strategies to enhance human performance and health
On the existence of 0/1 polytopes with high semidefinite extension complexity
In Rothvo\ss{} it was shown that there exists a 0/1 polytope (a polytope
whose vertices are in \{0,1\}^{n}) such that any higher-dimensional polytope
projecting to it must have 2^{\Omega(n)} facets, i.e., its linear extension
complexity is exponential. The question whether there exists a 0/1 polytope
with high PSD extension complexity was left open. We answer this question in
the affirmative by showing that there is a 0/1 polytope such that any
spectrahedron projecting to it must be the intersection of a semidefinite cone
of dimension~2^{\Omega(n)} and an affine space. Our proof relies on a new
technique to rescale semidefinite factorizations
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