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

Iatrogenic Vascular Injuries in Sweden. A Nationwide Study 1987–2005

ObjectivesTo study the epidemiology of vascular injuries, with special focus on Iatrogenic Vascular Injuries (IVIs) and time-trends.Design and methodsFrom the Swedish national vascular registry, Swedvasc, prospectively registered data on vascular injuries during 1987–2005 were analysed and cross-referenced for mortalityagainst the population registry.ResultsOf 1853 injuries, 48% were caused by iatrogenic, 29% penetrating and 23% blunt trauma. In the three groups median age was 68, 35 and 40 years, respectively. The annual incidence of procedures for vascular injuries increased from 1.2–1.6 per 100 000 inhabitants and the proportion of IVIs increased from 41 to 51%, during the period. Mortality was higher after IVI (4.9%) compared to non-IVI (2.5%). Patients with IVI also had more co-morbidities; 58% cardiac disease, 44% hypertension, and 18% renal dysfunction.Among 888 IVIs, right femoral arterial injury was the most frequent (37%). The most common vascular reconstruction was direct suture (39%) followed by by-pass or interposition graft (19%, of which prosthetics were used in over half the cases). Endovascular repair increased from 4.6% to 15% between 1987 and 2005.ConclusionsVascular injuries, in particular iatrogenic ones, appear to be increasing. Iatrogenic injuries affect vulnerable patients with co-morbidities and are associated with a high mortality

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

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

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

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