2,419 research outputs found
Quantum Games
In these lecture notes we investigate the implications of the identification
of strategies with quantum operations in game theory beyond the results
presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83,
3077 (1999)]. After introducing a general framework, we study quantum games
with a classical analogue in order to flesh out the peculiarities of game
theoretical settings in the quantum domain. Special emphasis is given to a
detailed investigation of different sets of quantum strategies.Comment: 13 pages (LaTeX), 3 figure
Fidelity and Concurrence of conjugated states
We prove some new properties of fidelity (transition probability) and
concurrence, the latter defined by straightforward extension of Wootters
notation. Choose a conjugation and consider the dependence of fidelity or of
concurrence on conjugated pairs of density operators. These functions turn out
to be concave or convex roofs. Optimal decompositions are constructed. Some
applications to two- and tripartite systems illustrate the general theorem.Comment: 10 pages, RevTex, Correction: Enlarged, reorganized version. More
explanation
Trade-off between multiple-copy transformation and entanglement catalysis
We demonstrate that multiple copies of a bipartite entangled pure state may
serve as a catalyst for certain entanglement transformations while a single
copy cannot. Such a state is termed a "multiple-copy catalyst" for the
transformations. A trade-off between the number of copies of source state and
that of the catalyst is also observed. These results can be generalized to
probabilistic entanglement transformations directly.Comment: Essentially the journal version. 7 pages, no figures. Minor
correction
Multiple-copy entanglement transformation and entanglement catalysis
We prove that any multiple-copy entanglement transformation [S.
Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A \textbf{65}, 052315
(2002)] can be implemented by a suitable entanglement-assisted local
transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. \textbf{83},
3566 (1999)]. Furthermore, we show that the combination of multiple-copy
entanglement transformation and the entanglement-assisted one is still
equivalent to the pure entanglement-assisted one. The mathematical structure of
multiple-copy entanglement transformations then is carefully investigated. Many
interesting properties of multiple-copy entanglement transformations are
presented, which exactly coincide with those satisfied by the
entanglement-assisted ones. Most interestingly, we show that an arbitrarily
large number of copies of state should be considered in multiple-copy
entanglement transformations.Comment: 11 pages, RevTex 4. Main results unchanged. Journal versio
Catalysis in non--local quantum operations
We show how entanglement can be used, without being consumed, to accomplish
unitary operations that could not be performed with out it. When applied to
infinitesimal transformations our method makes equivalent, in the sense of
Hamiltonian simulation, a whole class of otherwise inequivalent two-qubit
interactions. The new catalysis effect also implies the asymptotic equivalence
of all such interactions.Comment: 4 pages, revte
Positive maps, majorization, entropic inequalities, and detection of entanglement
In this paper, we discuss some general connections between the notions of
positive map, weak majorization and entropic inequalities in the context of
detection of entanglement among bipartite quantum systems. First, basing on the
fact that any positive map can
be written as the difference between two completely positive maps
, we propose a possible way to generalize the
Nielsen--Kempe majorization criterion. Then we present two methods of
derivation of some general classes of entropic inequalities useful for the
detection of entanglement. While the first one follows from the aforementioned
generalized majorization relation and the concept of the Schur--concave
decreasing functions, the second is based on some functional inequalities. What
is important is that, contrary to the Nielsen--Kempe majorization criterion and
entropic inequalities, our criteria allow for the detection of entangled states
with positive partial transposition when using indecomposable positive maps. We
also point out that if a state with at least one maximally mixed subsystem is
detected by some necessary criterion based on the positive map , then
there exist entropic inequalities derived from (by both procedures)
that also detect this state. In this sense, they are equivalent to the
necessary criterion [I\ot\Lambda](\varrho_{AB})\geq 0. Moreover, our
inequalities provide a way of constructing multi--copy entanglement witnesses
and therefore are promising from the experimental point of view. Finally, we
discuss some of the derived inequalities in the context of recently introduced
protocol of state merging and possibility of approximating the mean value of a
linear entanglement witness.Comment: the published version, 25 pages in NJP format, 6 figure
Quantifying Graft Detachment after Descemet's Membrane Endothelial Keratoplasty with Deep Convolutional Neural Networks
Purpose: We developed a method to automatically locate and quantify graft
detachment after Descemet's Membrane Endothelial Keratoplasty (DMEK) in
Anterior Segment Optical Coherence Tomography (AS-OCT) scans. Methods: 1280
AS-OCT B-scans were annotated by a DMEK expert. Using the annotations, a deep
learning pipeline was developed to localize scleral spur, center the AS-OCT
B-scans and segment the detached graft sections. Detachment segmentation model
performance was evaluated per B-scan by comparing (1) length of detachment and
(2) horizontal projection of the detached sections with the expert annotations.
Horizontal projections were used to construct graft detachment maps. All final
evaluations were done on a test set that was set apart during training of the
models. A second DMEK expert annotated the test set to determine inter-rater
performance. Results: Mean scleral spur localization error was 0.155 mm,
whereas the inter-rater difference was 0.090 mm. The estimated graft detachment
lengths were in 69% of the cases within a 10-pixel (~150{\mu}m) difference from
the ground truth (77% for the second DMEK expert). Dice scores for the
horizontal projections of all B-scans with detachments were 0.896 and 0.880 for
our model and the second DMEK expert respectively. Conclusion: Our deep
learning model can be used to automatically and instantly localize graft
detachment in AS-OCT B-scans. Horizontal detachment projections can be
determined with the same accuracy as a human DMEK expert, allowing for the
construction of accurate graft detachment maps. Translational Relevance:
Automated localization and quantification of graft detachment can support DMEK
research and standardize clinical decision making.Comment: To be published in Translational Vision Science & Technolog
Body mass index, waist circumference, waist-hip ratio, and glucose intolerance in Chinese and Europid adults in Newcastle, UK.
OBJECTIVE: To compare the prevalence of glucose intolerance (impaired glucose tolerance and diabetes), and its relationship to body mass index (BMI) and waist-hip ratio in Chinese and Europid adults. DESIGN: This was a cross sectional study. SETTING: Newcastle upon Tyne. SUBJECTS: These comprised Chinese and Europid men and women, aged 25-64 years, and resident in Newcastle upon Tyne, UK. MAIN OUTCOME MEASURES: Two hour post load plasma glucose concentration, BMI, waist circumference, and waist-hip ratio. METHODS: Population based samples of Chinese and European adults were recruited. Each subject had a standard WHO oral glucose tolerance test. RESULTS: Complete data were available for 375 Chinese and 610 Europid subjects. The age adjusted prevalences of glucose intolerance in Chinese and Europid men were 13.0% (p = 0.04). Mean BMIs were lower in Chinese men (23.8 v 26.1) and women (23.5 v 26.1) than in the Europids (p values < 0.001), as were waist circumferences (men, 83.3 cm v 90.8, p < 0.001; women, 77.3 cm v 79.2, p < 0.05). Mean waist-hip ratios were lower in Chinese men (0.90 v 0.91, p = 0.02) but higher in Chinese women (0.84 v 0.78, p < 0.001) compared with Europids. In both Chinese and Europid adults, higher BMI, waist circumference, and waist-hip ratio were associated with glucose intolerance. CONCLUSIONS: The prevalence of glucose intolerance in Chinese men and women, despite lower BMIs, is similar to or higher than that in local Europid men and women and intermediate between levels found in China and those in Mauritius. It is suggested that an increase in mean BMI to the levels in the Europid population will be associated with a substantial increase in glucose intolerance in Chinese people
Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings
The class of generalized shearlet dilation groups has recently been developed
to allow the unified treatment of various shearlet groups and associated
shearlet transforms that had previously been studied on a case-by-case basis.
We consider several aspects of these groups: First, their systematic
construction from associative algebras, secondly, their suitability for the
characterization of wavefront sets, and finally, the question of constructing
embeddings into the symplectic group in a way that intertwines the
quasi-regular representation with the metaplectic one. For all questions, it is
possible to treat the full class of generalized shearlet groups in a
comprehensive and unified way, thus generalizing known results to an infinity
of new cases. Our presentation emphasizes the interplay between the algebraic
structure underlying the construction of the shearlet dilation groups, the
geometric properties of the dual action, and the analytic properties of the
associated shearlet transforms.Comment: 28 page
Characterizing mixing and measurement in quantum mechanics
What fundamental constraints characterize the relationship between a mixture
of quantum states, the states being mixed,
and the probabilities ? What fundamental constraints characterize the
relationship between prior and posterior states in a quantum measurement? In
this paper we show that there are many surprisingly strong constraints on these
mixing and measurement processes that can be expressed simply in terms of the
eigenvalues of the quantum states involved. These constraints capture in a
succinct fashion what it means to say that a quantum measurement acquires
information about the system being measured, and considerably simplify the
proofs of many results about entanglement transformation.Comment: 12 page
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