Optimal quantum state discrimination via nested binary measurements

A method to compute the optimal success probability of discrimination of N arbitrary quantum states is presented, based on the decomposition of any N-outcome measurement into sequences of nested two-outcome ones. In this way the optimization of the measurement operators can be carried out in successive steps, optimizing first the binary measurements at the deepest nesting level and then moving on to those at higher levels. We obtain an analytical expression for the maximum success probability after the first optimization step and examine its form for the specific case of N=3,4 states of a qubit. In this case, at variance with previous proposals, we are able to provide a compact expression for the success probability of any set of states, whose numerical optimization is straightforward; the results thus obtained highlight some lesser-known features of the discrimination problem.Comment: v2: added references to previous works closely related to Sec. II; 8+3 pages; 3 figure

On the Probability of Generating a Lattice

We study the problem of determining the probability that m vectors selected uniformly at random from the intersection of the full-rank lattice L in R^n and the window [0,B)^n generate $\Lambda$ when B is chosen to be appropriately large. This problem plays an important role in the analysis of the success probability of quantum algorithms for solving the Discrete Logarithm Problem in infrastructures obtained from number fields and also for computing fundamental units of number fields. We provide the first complete and rigorous proof that 2n+1 vectors suffice to generate L with constant probability (provided that B is chosen to be sufficiently large in terms of n and the covering radius of L and the last n+1 vectors are sampled from a slightly larger window). Based on extensive computer simulations, we conjecture that only n+1 vectors sampled from one window suffice to generate L with constant success probability. If this conjecture is true, then a significantly better success probability of the above quantum algorithms can be guaranteed.Comment: 18 page

Quantum Random Access Codes with Shared Randomness

We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79) QRACs match this upper bound). We discuss some particular constructions for several small values of n. We also study the classical counterpart of this model where n bits are encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal construction for such codes and find their success probability exactly--it is less than in the quantum case. Interactive 3D quantum random access codes are available on-line at http://home.lanet.lv/~sd20008/racs .Comment: 51 pages, 33 figures. New sections added: 1.2, 3.5, 3.8.2, 5.4 (paper appears to be shorter because of smaller margins). Submitted as M.Math thesis at University of Waterloo by M

The relationship between career strategies and career success

This study examined the relationship between career strategies and career success. The three dimensions that measured career strategies were enhancing promotability, strengthening external contacts, and improving image with superiors. Meanwhile, the dimension that measured career success was subjective career success. Data were gathered through questionnaires administered to employees at a manufacturing organisation (n=185). Correlation and regression analyses were used to examine the relationship between career strategies and career success. The results indicated that there were no relationship between career strategies and career success. Only two of the career strategy dimensions were positively correlated with career success, namely strengthening external contacts and improving image with superiors. The multi-regression results suggested that improving image with superiors was the most important factor in influencing individual’s career success. The findings were discussed and recommendations for future research were also addressed

The effects of clinical hypnosis versus Neurolinguistic Programming (NLP) before External Cephalic Version (ECV) : a prospective off-centre randomised, double-blind, controlled trial

Objective. To examine the effects of clinical hypnosis versus NLP intervention on the success rate of ECV procedures in comparison to a control group. Methods. A prospective off-centre randomised trial of a clinical hypnosis intervention against NLP of women with a singleton breech fetus at or after 370/7 (259 days) weeks of gestation and normal amniotic fluid index. All 80 participants heard a 20-minute recorded intervention via head phones. Main outcome assessed was success rate of ECV. The intervention groups were compared with a control group with standard medical care alone (n=122). Results. A total of 42 women, who received a hypnosis intervention prior to ECV, had a 40.5% (n=17), successful ECV, whereas 38 women, who received NLP, had a 44.7% (n=17) successful ECV (P > 0.05). The control group had similar patient characteristics compared to the intervention groups (P > 0.05). In the control group (n = 122) 27.3% (n = 33) had a statistically significant lower successful ECV procedure than NLP (P = 0.05) and hypnosis and NLP (P = 0.03). Conclusions. These findings suggest that prior clinical hypnosis and NLP have similar success rates of ECV procedures and are both superior to standard medical care alone

The relationship between terms-of-trade and trade balance in ASEAN-5

This study examines the relationship between career strategies and career success. The three dimensions that measured career strategies were enhancing promotability, strengthening external contacts, and improving image with superiors. Meanwhile, the dimension that measured career success was subjective career success. Data were gathered through the distribution of questionnaires to employees at a manufacturing organization (n=185). Correlation and regression analysis were used to examine the relationship between career strategies and career success. The results indicated that there were no relationships between overall career strategies and career success. However, in terms of career strategies dimensions, only two were positively correlated with career success, namely, strengthening external contacts and improving image with superiors. The multi-regression results suggest that improving image with superiors was the most important factor in influencing individual’s career success. The findings were discussed and recommendations for future research were also put forward

Stochastic domination and weak convergence of conditioned Bernoulli random vectors

For n>=1 let X_n be a vector of n independent Bernoulli random variables. We assume that X_n consists of M "blocks" such that the Bernoulli random variables in block i have success probability p_i. Here M does not depend on n and the size of each block is essentially linear in n. Let X'_n be a random vector having the conditional distribution of X_n, conditioned on the total number of successes being at least k_n, where k_n is also essentially linear in n. Define Y'_n similarly, but with success probabilities q_i>=p_i. We prove that the law of X'_n converges weakly to a distribution that we can describe precisely. We then prove that sup Pr(X'_n <= Y'_n) converges to a constant, where the supremum is taken over all possible couplings of X'_n and Y'_n. This constant is expressed explicitly in terms of the parameters of the system.Comment: 39 pages, 2 figure

Outcome of secondary root canal treatment: a systematic review of the literature.

UNLABELLED: AIMS (I): To investigate the effects of study characteristics on the reported success rates of secondary root canal treatment (2 degrees RCT or root canal retreatment); and (ii) to investigate the effects of clinical factors on the success of 2 degrees RCT. METHODOLOGY: Longitudinal human clinical studies investigating outcome of 2 degrees RCT which were published upto the end of 2006 were identified electronically (MEDLINE and Cochrane database 1966-2006 Dec, week 4). Four journals (Dental Traumatology, International Endodontic Journal, Journal of Endodontics, Oral Surgery Oral Medicine Oral Pathology Endodontics Radiology), bibliographies of all relevant papers and review articles were hand-searched. Two reviewers (Y-LN, KG) independently assessed and selected the studies based on specified inclusion criteria and extracted the data onto a pre-designed proforma, independently. The criteria were: (i) Clinical studies on 2 degrees RCT; (ii) Stratified analyses available for 2 degrees RCT where 1 degrees RCT data included; (iii) Sample size given and larger than 10; (iv) At least 6-month post-operative review; (v) Success based on clinical and/or radiographic criteria (strict = absence of apical radiolucency; loose = reduction in size of radiolucency); and (vi) Overall success rate given or could be calculated from the raw data. Three strands of evidence or analyses were used to triangulate a consensus view. The reported findings from individual studies, including those excluded for quantitative analysis, were utilized for the intuitive synthesis which constituted the first strand of evidence. Secondly, the pooled weighted success rates by each study characteristic and potential prognostic factor were estimated using the random effect model. Thirdly, the effects of study characteristics and prognostic factors (expressed as odds ratios) on success rates were estimated using fixed and random effects meta-analysis with DerSimonean and Laird's methods. Meta-regression models were used to explore potential sources of statistical heterogeneity. Study characteristics considered in the meta-regression analyses were: decade of publication, study-specific criteria for success (radiographic, combined radiographic & clinical), unit of outcome measure (tooth, root), duration after treatment when assessing success ('at least 4 years' or '<4 years'), geographic location of the study (North American, Scandinavian, other countries), and qualification of the operator (undergraduate students, postgraduate students, general dental practitioners, specialist or mixed group). RESULTS: Of the 40 papers identified, 17 studies published between 1961 and 2005 were included; none were published in 2006. The majority of studies were retrospective (n = 12) and only five prospective. The pooled weighted success rate of 2 degrees RCT judged by complete healing was 76.7% (95% CI 73.6%, 89.6%) and by incomplete healing, 77.2% (95% CI 61.1%, 88.1%). The success rates by 'decade of publication' and 'geographic location of study' were not significantly different at the 5% level. Eighteen clinical factors had been investigated in various combinations in previous studies. The most frequently and thoroughly investigated were 'periapical status' (n = 13), 'size of lesion' (n = 7), and 'apical extent of RF' (n = 5) which were found to be significant prognostic factors. The effect of different aspects of primary treatment history and re-treatment procedures has been poorly tested. CONCLUSIONS: The pooled estimated success rate of secondary root canal treatment was 77%. The presence of pre-operative periapical lesion, apical extent of root filling and quality of coronal restoration proved significant prognostic factors with concurrence between all three strands of evidence whilst the effects of 1 degrees RCT history and 2 degrees RCT protocol have been poorly investigated

Anatomic Success of Scleral Buckling for Rhegmatogenous Retinal Detachment - A Retrospective Study of 524 Cases

Background/Aim: Our purpose was to investigate the anatomic success of scleral buckling surgery for rhegmatogenous retinal detachment. Material and Methods: A total of 524 consecutive patients were retrospectively analysed. Several parameters including the lens status, number of breaks and extent of retinal detachment, preoperative proliferative vitreoretinopathy and refractive errors were examined. The minimum follow-up was 6 months. The primary success rate was defined as anatomic success being stable over a period of at least 6 months after surgery. The secondary success rate was defined as anatomic success after the second intervention if necessary. Besides an analysis over all patients, the patients were grouped according to the severity of the preoperative situation in simple, medium and severe cases. Results: The overall primary anatomic success rate was 84.7% and the secondary success rate 96.4% after 1 initial scleral buckling surgery and 1 additional surgery in case of persisting retinal detachment, and 19.1% of the patients with an initially attached retina after 1 scleral buckling surgery experienced a redetachment in the postoperative course and were successfully treated in 60/85 cases. In phakic patients (n = 359) the primary success rate was 89.7%, whereas in pseudophakic patients (n = 165) a primary success rate of 73.9% was obtained. The primary success was additionally influenced by the extent of the retinal detachment measured in clock hours (p <0.001), undetected holes (p = 0.004), small (p = 0.037) and no gas tamponade (p = 0.021). In simple, medium and severe cases, phakic patients always achieved better anatomic results (89.9, 89.1 and 90.2%) compared to pseudophakic ones (82.5, 70.3 and 36.4%). Conclusion: Scleral buckling is a very good surgical option in phakic patients irrespective of the preoperative severity and simple cases in pseudophakic patients. Scleral buckling represents a surgical technique worth being trained and performed in the light of favourable results especially in phakic eyes. Copyright (C) 2010 S. Karger AG, Base