The learnability of unknown quantum measurements

© Rinton Press. In this work, we provide an elegant framework to analyze learning matrices in the Schatten class by taking advantage of a recently developed methodology—matrix concentration inequalities. We establish the fat-shattering dimension, Rademacher/Gaussian complexity, and the entropy number of learning bounded operators and trace class operators. By characterising the tasks of learning quantum states and two-outcome quantum measurements into learning matrices in the Schatten-1 and ∞ classes, our proposed approach directly solves the sample complexity problems of learning quantum states and quantum measurements. Our main result in the paper is that, for learning an unknown quantum measurement, the upper bound, given by the fat-shattering dimension, is linearly proportional to the dimension of the underlying Hilbert space. Learning an unknown quantum state becomes a dual problem to ours, and as a byproduct, we can recover Aaronson’s famous result [Proc. R. Soc. A 463, 3089–3144 (2007)] solely using a classical machine learning technique. In addition, other famous complexity measures like covering numbers and Rademacher/Gaussian complexities are derived explicitly under the same framework. We are able to connect measures of sample complexity with various areas in quantum information science, e.g. quantum state/measurement tomography, quantum state discrimination and quantum random access codes, which may be of independent interest. Lastly, with the assistance of general Bloch-sphere representation, we show that learning quantum measurements/states can be mathematically formulated as a neural network. Consequently, classical ML algorithms can be applied to efficiently accomplish the two quantum learning tasks

Patient complexity and genotype-phenotype correlations in biliary atresia: a cross-sectional analysis

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Loss of AQP3 protein expression is associated with worse progression-free and cancer-specific survival in patients with muscle-invasive bladder cancer

Purpose Urothelial carcinoma has recently been shown to express several aquaporins (AQP), with AQP3 being of particular interest as its expression is reduced or lost in tumours of higher grade and stage. Loss of AQP3 expression was associated with worse progression-free survival (PFS) in patients with pT1 bladder cancer. The objective of this study was to investigate the prognostic value of AQP3 expression in patients with muscle-invasive bladder carcinoma (MIBC). Methods Retrospective single-centre analysis of the oncological outcome of patients following radical cystectomy (Cx) due to MIBC. Immunohistochemistry was used to assess AQP3 protein expression in 100 Cx specimens. Expression levels of AQP3 were related to clinicopathological variables. The impact of biomarker expression on progression-free, cancer-specific and overall survival was determined by multivariate Cox regression analysis (MVA). Results High expression of AQP3 by the tumour was associated with a statistically significantly improved PFS (75 vs. 19 %, p = 0.043) and CSS (75 vs. 18 %, p = 0.030) and, alongside lymph node involvement, was an independent predictor of PFS (HR 2.871, CI 1.066–7.733, p = 0.037), CSS (HR 3.325, CI 1.204–8.774, p = 0.019) and OS (HR 2.001, CI 1.014–3.947) in MVA. Conclusions Although the results of the study would be strengthened by a larger, more appropriately powered, prospective, multi-institutional study, our findings strongly suggest that AQP3 expression status may represent an independent predictor of PFS and CSS in MIBC and may help select patients in need for (neo-)adjuvant chemotherapy

Identification and characterization of a novel incompatibility group X3 plasmid carrying blaNDM-1 in Enterobacteriaceae isolates with epidemiological links to multiple geographical areas in China

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No entropy enigmas for N=4 dyons

We explain why multi-centered black hole configurations where at least one of the centers is a large black hole do not contribute to the indexed degeneracies in theories with N=4 supersymmetry. This is a consequence of the fact that such configurations, although supersymmetric, belong to long supermultiplets. As a result, there is no entropy enigma in N=4 theories, unlike in N=2 theories.Comment: 14 page

Comparison of the outcome of living related donor and cadaveric renal transplantation in Queen Mary Hospital - a single centre experience

Living related donors (LRD) have been the main source of donor kidneys in Hong Kong. In recent years, there has been an increase in the proportion of cadaveric (CAD) kidneys transplantation. This review examines the results of renal transplantation in. Queen Mary Hospital (QMH) in order to assess the continuing need for LRD kidney transplantation. The records of 159 of 165 transplant cases between 1983 and 1991 were analyzed. The mean age of recipients was 35.6 years (range 11 to 57), with a male predominance in the LED recipients (p = 0.03). The waiting time for the LRD recipients was significantly less than the CAD recipients (p < 0.001). There was no difference in the distribution of different primary renal diseases causing end stage renal failure between the LRD and CAD groups. The cumulative graft survival at five years was 82.5% and 65.8% for LRD and CAD respectively (p = 0.02), Graft function was also significantly better in LRD recipients (p < 0,01), Early surgical complications were more common after CAD transplantation (14% vs 29%, p = 0.02). While the transplant centres and the Hong Kong Government continue to promote cadaveric organ donation, the LRD transplant programme should be equally encouraged because of superior graft outcome.published_or_final_versio

Tunable Multifunctional Topological Insulators in Ternary Heusler Compounds

Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude of spin-orbit coupling (by the atomic charge). Based on the first-principle calculations we demonstrate that around fifty Heusler compounds show the band inversion similar to HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare earth element Ln which can realize additional properties ranging from superconductivity (e. g. LaPtBi[12]) to magnetism (e. g. GdPtBi[13]) and heavy-fermion behavior (e. g. YbPtBi[14]). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.Comment: 20 pages, 5 figure

Patient complexity and genotype-phenotype correlations in biliary atresia: a cross-sectional analysis

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Genetic study of congenital bile-duct dilatation identifies de novo and inherited variants in functionally related genes

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