5,141 research outputs found
On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback
© 1963-2012 IEEE. We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions
Lorentz Beams
A new kind of tridimensional scalar optical beams is introduced. These beams
are called Lorentz beams because the form of their transverse pattern in the
source plane is the product of two independent Lorentz functions. Closed-form
expression of free-space propagation under paraxial limit is derived and pseudo
non-diffracting features pointed out. Moreover, as the slowly varying part of
these fields fulfils the scalar paraxial wave equation, it follows that there
exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original
Lorentz beam to a Gaussian apodization function. Although the existence of
Lorentz-Gauss beams can be shown by using two different and independent ways
obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega
et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different
approach, which makes use of Lie's group theory, and which possesses the merit
to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics
Multi-core job submission and grid resource scheduling for ATLAS AthenaMP
AthenaMP is the multi-core implementation of the ATLAS software framework and allows the efficient sharing of memory pages between multiple threads of execution. This has now been validated for production and delivers a significant reduction on the overall application memory footprint with negligible CPU overhead. Before AthenaMP can be routinely run on the LHC Computing Grid it must be determined how the computing resources available to ATLAS can best exploit the notable improvements delivered by switching to this multi-process model. A study into the effectiveness and scalability of AthenaMP in a production environment will be presented. Best practices for configuring the main LRMS implementations currently used by grid sites will be identified in the context of multi-core scheduling optimisation
Longitudinal LASSO: Jointly Learning Features and Temporal Contingency for Outcome Prediction
Longitudinal analysis is important in many disciplines, such as the study of
behavioral transitions in social science. Only very recently, feature selection
has drawn adequate attention in the context of longitudinal modeling. Standard
techniques, such as generalized estimating equations, have been modified to
select features by imposing sparsity-inducing regularizers. However, they do
not explicitly model how a dependent variable relies on features measured at
proximal time points. Recent graphical Granger modeling can select features in
lagged time points but ignores the temporal correlations within an individual's
repeated measurements. We propose an approach to automatically and
simultaneously determine both the relevant features and the relevant temporal
points that impact the current outcome of the dependent variable. Meanwhile,
the proposed model takes into account the non-{\em i.i.d} nature of the data by
estimating the within-individual correlations. This approach decomposes model
parameters into a summation of two components and imposes separate block-wise
LASSO penalties to each component when building a linear model in terms of the
past measurements of features. One component is used to select features
whereas the other is used to select temporal contingent points. An accelerated
gradient descent algorithm is developed to efficiently solve the related
optimization problem with detailed convergence analysis and asymptotic
analysis. Computational results on both synthetic and real world problems
demonstrate the superior performance of the proposed approach over existing
techniques.Comment: Proceedings of the 21th ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining. ACM, 201
On the Minimum Degree up to Local Complementation: Bounds and Complexity
The local minimum degree of a graph is the minimum degree reached by means of
a series of local complementations. In this paper, we investigate on this
quantity which plays an important role in quantum computation and quantum error
correcting codes. First, we show that the local minimum degree of the Paley
graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge,
the highest known bound on an explicit family of graphs. Probabilistic methods
allows us to derive the existence of an infinite number of graphs whose local
minimum degree is linear in their order with constant 0.189 for graphs in
general and 0.110 for bipartite graphs. As regards the computational complexity
of the decision problem associated with the local minimum degree, we show that
it is NP-complete and that there exists no k-approximation algorithm for this
problem for any constant k unless P = NP.Comment: 11 page
Estimation of pure qubits on circles
Gisin and Popescu [PRL, 83, 432 (1999)] have shown that more information
about their direction can be obtained from a pair of anti-parallel spins
compared to a pair of parallel spins, where the first member of the pair (which
we call the pointer member) can point equally along any direction in the Bloch
sphere. They argued that this was due to the difference in dimensionality
spanned by these two alphabets of states. Here we consider similar alphabets,
but with the first spin restricted to a fixed small circle of the Bloch sphere.
In this case, the dimensionality spanned by the anti-parallel versus parallel
alphabet is now equal. However, the anti-parallel alphabet is found to still
contain more information in general. We generalize this to having N parallel
spins and M anti-parallel spins. When the pointer member is restricted to a
small circle these alphabets again span spaces of equal dimension, yet in
general, more directional information can be found for sets with smaller |N-M|
for any fixed total number of spins. We find that the optimal POVMs for
extracting directional information in these cases can always be expressed in
terms of the Fourier basis. Our results show that dimensionality alone cannot
explain the greater information content in anti-parallel combinations of spins
compared to parallel combinations. In addition, we describe an LOCC protocol
which extract optimal directional information when the pointer member is
restricted to a small circle and a pair of parallel spins are supplied.Comment: 23 pages, 8 figure
Bipartite quantum states and random complex networks
We introduce a mapping between graphs and pure quantum bipartite states and
show that the associated entanglement entropy conveys non-trivial information
about the structure of the graph. Our primary goal is to investigate the family
of random graphs known as complex networks. In the case of classical random
graphs we derive an analytic expression for the averaged entanglement entropy
while for general complex networks we rely on numerics. For large
number of nodes we find a scaling where both
the prefactor and the sub-leading O(1) term are a characteristic of
the different classes of complex networks. In particular, encodes
topological features of the graphs and is named network topological entropy.
Our results suggest that quantum entanglement may provide a powerful tool in
the analysis of large complex networks with non-trivial topological properties.Comment: 4 pages, 3 figure
Some families of density matrices for which separability is easily tested
We reconsider density matrices of graphs as defined in [quant-ph/0406165].
The density matrix of a graph is the combinatorial laplacian of the graph
normalized to have unit trace. We describe a simple combinatorial condition
(the "degree condition") to test separability of density matrices of graphs.
The condition is directly related to the PPT-criterion. We prove that the
degree condition is necessary for separability and we conjecture that it is
also sufficient. We prove special cases of the conjecture involving nearest
point graphs and perfect matchings. We observe that the degree condition
appears to have value beyond density matrices of graphs. In fact, we point out
that circulant density matrices and other matrices constructed from groups
always satisfy the condition and indeed are separable with respect to any
split. The paper isolates a number of problems and delineates further
generalizations.Comment: 14 pages, 4 figure
A general algorithm for manipulating non-linear and linear entanglement witnesses by using exact convex optimization
A generic algorithm is developed to reduce the problem of obtaining linear
and nonlinear entanglement witnesses of a given quantum system, to convex
optimization problem. This approach is completely general and can be applied
for the entanglement detection of any N-partite quantum system. For this
purpose, a map from convex space of separable density matrices to a convex
region called feasible region is defined, where by using exact convex
optimization method, the linear entanglement witnesses can be obtained from
polygonal shape feasible regions, while for curved shape feasible regions,
envelope of the family of linear entanglement witnesses can be considered as
nonlinear entanglement witnesses. This method proposes a new methodological
framework within which most of previous EWs can be studied. To conclude and in
order to demonstrate the capability of the proposed approach, besides providing
some nonlinear witnesses for entanglement detection of density matrices in
unextendible product bases, W-states, and GHZ with W-states, some further
examples of three qubits systems and their classification and entanglement
detection are included. Also it is explained how one can manipulate most of the
non-decomposable linear and nonlinear three qubits entanglement witnesses
appearing in some of the papers published by us and other authors, by the
method proposed in this paper. Keywords: non-linear and linear entanglement
witnesses, convex optimization. PACS number(s): 03.67.Mn, 03.65.UdComment: 37 page
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