Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C^n tensor C^n whose operator-Schmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number S for every S in {1,...,9}. This corollary was unexpected, since it contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003) 052301] based on intuition from a striking result in the two-qubit case. By the results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901 quant-ph/0112124], who also considered the two-qubit case, our result implies that there are nine equivalence classes of unitaries on C^3 tensor C^3 which are probabilistically interconvertible by (stochastic) local operations and classical communication. As another corollary, a prescription is produced for constructing maximally-entangled operators from biunimodular functions. Reversing tact, we state a generalized operator-Schmidt decomposition of the quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 --> C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by Nielsen's bound) that the communication cost of the QFT remains maximal when a net transfer of qudits is permitted. In an appendix, a canonical procedure is given for removing basis-dependence for results and proofs depending on the "magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum and Reversible Computation at Stony Brook May 31, 2003. The talk slides and audio are available at http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos and minor cosmetic

Evolution of the interfacial structure of LaAlO3 on SrTiO3

The evolution of the atomic structure of LaAlO3 grown on SrTiO3 was investigated using surface x-ray diffraction in conjunction with model-independent, phase-retrieval algorithms between two and five monolayers film thickness. A depolarizing buckling is observed between cation and oxygen positions in response to the electric field of polar LaAlO3, which decreases with increasing film thickness. We explain this in terms of competition between elastic strain energy, electrostatic energy, and electronic reconstructions. The findings are qualitatively reproduced by density-functional theory calculations. Significant cationic intermixing across the interface extends approximately three monolayers for all film thicknesses. The interfaces of films thinner than four monolayers therefore extend to the surface, which might affect conductivity

Short-term effects of a pay-for-performance programme for diabetes in a primary care setting: an observational study

Objective A pay-for-performance (P4P) programme for primary care was introduced in 2011 by a Swedish county (with 1.6 million inhabitants). Effects on register entry practice and comparability of data for patients with diabetes mellitus were assessed. Design and setting Observational study analysing short-term outcomes before and after introduction of a P4P programme in the study county as compared with a reference county. Subjects A total of 84 053 patients reported to the National Diabetes Register by 349 primary care units. Main outcome measures Completeness of data, level and target achievement of glycated haemoglobin (HbA1c), blood pressure (BP), and LDL cholesterol (LDL). Results In the study county, newly recruited patients who were entered during the incentive programme were less well controlled than existing patients in the register - they had higher HbA1c (54.9 [54.5-55.4] vs. 53.7 [53.6-53.9] mmol/mol), BP, and LDL. The percentage of patients with entry of BP, HbA1c, LDL, albuminuria, and smoking increased in the study county but not in the reference county (+26.3% vs -1.5%). In the study county, with an incentive for BP < 130/80 mmHg, BP data entry behaviour was altered with an increased preference for sub-target BP values and a decline in zero end-digit readings (38.3% vs. 33.7%, p < 0.001). Conclusion P4P led to increased register entry, increased completeness of data, and altered BP entry behaviour. Analysis of newly added patients and data shows that missing patients and data can cause performance to be overestimated. Potential effects on reporting quality should be considered when designing payment programmes. Key points A pay-for-performance programme, with a focus on data entry, was introduced in a primary care region in Sweden. Register data entry in the National Diabetes Register increased and registration behaviour was altered, especially for blood pressure. Newly entered patients and data during the incentive programme were less well controlled. Missing data in a quality register can cause performance to be overestimated

Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier

In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is completely random, or unbiased. For N-level systems, the 6-level ones are the smallest for which a tomographically efficient set of N+1 mutually unbiased bases (MUBs) has not been found. To facilitate the search, we numerically extend the classification of unbiased bases, or Hadamards, by incrementally adjusting relative phases in a standard basis. We consider the non-unitarity caused by small adjustments with a second order Taylor expansion, and choose incremental steps within the 4-dimensional nullspace of the curvature. In this way we prescribe a numerical integration of a 4-parameter set of Hadamards of order 6.Comment: 5 pages, 2 figure

Unit cell of graphene on Ru(0001): a 25 x 25 supercell with 1250 carbon atoms

The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure has been determined, whereby 25 x 25 graphene unit cells lie on 23 x 23 unit cells of Ru. Each supercell contains 2 x 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers, and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C-C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.Comment: 9 pages, 3 figures, paper submitted to peer reviewed journa

Incidence of Acute Thrombo-Embolic Occlusion of the Superior Mesenteric Artery—A Population-based Study

AbstractObjective. To determine the incidence of acute thrombo-embolic occlusion of the superior mesenteric artery (AOSMA) in a population-based study.Material. All clinical (n=23,446) and forensic (n=7569) autopsies performed in the city of Malmö between 1970 and 1982 (population 264,000–230,000 inhabitants). The autopsy rate was 87%.Methods. Calculation of the incidence of AOSMA with intestinal gangrene in those autopsies coded for bowel ischaemia (997/23,446 clinical and 9/7569 forensic autopsies). The operative procedures performed in 1970, 1976 and 1982 were also analysed.Results. Two forensic and 211 clinical autopsies demonstrated AOSMA with intestinal gangrene. Previous suspicion of intestinal ischaemia was noted in only 33%. Sixteen patients were operated. The cause-specific mortality was 6.0/1000 deaths. The incidence was 8.6/100,000 person years, increasing exponentially with age (p<0.001). Mortality was 93%.Conclusions. The incidence and mortality of AOSMA is higher than previously reported from clinical series. There is seldom any suspicion of the diagnosis prior to death

Specific in vivo deletion of B-cell subpopulations expressing human immunoglobulins by the B-cell superantigen protein L

Some pathogens have evolved to produce proteins, called B-cell superantigens, that can interact with human immunoglobulin variable regions, independently of the combining site, and activate B lymphocytes that express the target immunoglobulins. However, the in vivo consequences of these interactions on human B-cell numbers and function are largely unknown. Using transgenic mice expressing fully human immunoglobulins, we studied the consequences of in vivo exposure of protein L of Peptostreptococcus magnus with human immunoglobulins. In the mature pool of B cells, protein L exposure resulted in a specific reduction of splenic marginal-zone B cells and peritoneal B-1 cells. Splenic B cells exhibited a skewed light-chain repertoire consistent with the capacity of protein L to bind specific kappa gene products. Remarkably, these two B-cell subsets are implicated in innate B-cell immunity, allowing rapid clearance of pathogens. Thus, the present study reveals a novel mechanism that may be used by some infectious agents to subvert a first line of the host's immune defense

Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and Theoretical (2007