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

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

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

Screening for Abdominal Aortic Aneurysm among Patients Referred to the Vascular Laboratory is Cost-effective

AbstractScreening for abdominal aortic aneurysm (AAA) in high-risk groups has been recommended based on a high prevalence of disease, while being questioned due to a high frequency of co-morbidities and inferior life-expectancy. We evaluated the long-term outcome and the cost-effectiveness of selective AAA screening among patients referred to the vascular laboratory for arterial examination.MethodsA total of 5924 patients, referred to the vascular laboratory of a university hospital, were screened for AAA with ultrasound (definition: ∅≥30mm), 1993–2005. Outcome data were gathered through hospital records and the national population registry. A Markov model was used for health–economic evaluation.ResultsAn AAA was detected in 181 patients (mean age 72.8 years), of whom 21.5% underwent elective repair (perioperative mortality 5.1%) after 7.5 years of follow-up. Four of six patients diagnosed with AAA rupture were operated upon. Relative 5-year survival compared with the general Swedish population, controlled for age and sex, was 80.4% (95% confidence interval (CI): 70.8–88.8). The cost-effectiveness was robust in base-case (11 084 Euro/life year gained) and in sensitivity analyses of prevalence, cost and survival.ConclusionsPatients in whom AAA was detected at selective screening had inferior long-term survival and were operated on less frequently, compared with AAA patients described in previous studies. Yet, selective screening at the vascular laboratory was cost-effective

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

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

Editor's Choice - European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Acute Limb Ischaemia

Peer reviewe

Spectrum of mutations in the CFTR gene of patients with classical and atypical forms of cystic fibrosis from southwestern Sweden: Identification of 12 novel mutations

Cystic fibrosis (CF) is caused by mutations in the CFTR gene. The spectrum of CFTR mutations varies between populations and depends on different factors, such as ethnic background and geographical location. The extensive CFTR mutation screening of 129 patients with classical or atypical CF from the south-western region of Sweden revealed the presence of 37 CFTR mutations, including 12 novel alleles. The overall mutation detection rate in this study population was 92%, the highest among all tested regions in Sweden. Eight mutations with a frequency above 1% (ΔF508, 394delTT, R117C, 3659delC, E60X, 1112delT, R764X, and 621 + 1G → T) accounted for 78% of CF chromosomes and have been recommended for inclusion in the CFTR mutation screening panel for molecular diagnosis of CF in this region. The multiple occurrence of specific CFTR alleles less common than the predominant ΔF508 mutation (394delTT, R117C, 3659delC) allowed for genotype-phenotype comparisons and revealed consistent relationships between these mutations and disease severity.published_or_final_versio

Proton-transfer pathways in the mitochondrial S. cerevisiae cytochrome c oxidase

In cytochrome c oxidase (CytcO) reduction of O2 to water is linked to uptake of eight protons from the negative side of the membrane: four are substrate protons used to form water and four are pumped across the membrane. In bacterial oxidases, the substrate protons are taken up through the K and the D proton pathways, while the pumped protons are transferred through the D pathway. On the basis of studies with CytcO isolated from bovine heart mitochondria, it was suggested that in mitochondrial CytcOs the pumped protons are transferred though a third proton pathway, the H pathway, rather than through the D pathway. Here, we studied these reactions in S. cerevisiae CytcO, which serves as a model of the mammalian counterpart. We analyzed the effect of mutations in the D (Asn99Asp and Ile67Asn) and H pathways (Ser382Ala and Ser458Ala) and investigated the kinetics of electron and proton transfer during the reaction of the reduced CytcO with O2. No effects were observed with the H pathway variants while in the D pathway variants the functional effects were similar to those observed with the R. sphaeroides CytcO. The data indicate that the S. cerevisiae CytcO uses the D pathway for proton uptake and presumably also for proton pumping