Radon-Nikodym derivatives of quantum operations

Given a completely positive (CP) map $T$, there is a theorem of the Radon-Nikodym type [W.B. Arveson, Acta Math. {\bf 123}, 141 (1969); V.P. Belavkin and P. Staszewski, Rep. Math. Phys. {\bf 24}, 49 (1986)] that completely characterizes all CP maps $S$ such that $T-S$ is also a CP map. This theorem is reviewed, and several alternative formulations are given along the way. We then use the Radon-Nikodym formalism to study the structure of order intervals of quantum operations, as well as a certain one-to-one correspondence between CP maps and positive operators, already fruitfully exploited in many quantum information-theoretic treatments. We also comment on how the Radon-Nikodym theorem can be used to derive norm estimates for differences of CP maps in general, and of quantum operations in particular.Comment: 22 pages; final versio

Entangling operations and their implementation using a small amount of entanglement

We study when a physical operation can produce entanglement between two systems initially disentangled. The formalism we develop allows to show that one can perform certain non-local operations with unit probability by performing local measurement on states that are weakly entangled.Comment: 4 pages, no figure

Entanglement cost of mixed states

We compute the entanglement cost of several families of bipartite mixed states, including arbitrary mixtures of two Bell states. This is achieved by developing a technique that allows us to ascertain the additivity of the entanglement of formation for any state supported on specific subspaces. As a side result, the proof of the irreversibility in asymptotic local manipulations of entanglement is extended to two-qubit systems.Comment: 4 pages, no figures, (v4) new results, including a new method to determine E_c for more general mixed states, presentation changed significantl

Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem

The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to O(d)-covariant channels this leads to a complete characterization and reveals a remarkable feature: instances of channels which are not in the convex hull of unitaries can return to it when either taking finitely many copies of them or supplementing with a completely depolarizing channel. In these scenarios this implies that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page

Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation

In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the minimum mean square error decreases with the order O(1/n).Comment: In this revision, some unlcear parts are clarifie

Platelet aggregation and risk of stent thrombosis or bleeding in interventionally treated diabetic patients with acute coronary syndrome

BACKGROUND: Platelet aggregation monitoring in diabetic patients treated with coronary interventions (PCI) for an acute coronary syndrome (ACS) is a promising way of optimizing treatment and outcomes in this high risk group. The aim of the study was to verify whether clopidogrel response measured by Multiplate analyzer (ADPtest) in diabetic ACS patients treated with PCI predicts the risk of stent thrombosis or cardiovascular mortality and bleeding. METHODS: Into this prospective, observational study 206 elective PCI patients were enrolled. Two cutoff points of ADPtest were used in analysis to divide patients into groups. One (345 AU x min) was calculated based on ROC curve analysis; this cutoff provided the best ROC curve fit, although it did not reach statistical significance. The other (468 AU x min) was accepted based on the consensus of the Working Group on On-Treatment Platelet Reactivity. The risk of stent thrombosis and mortality was assessed using Cox regression analysis and Kaplan-Meier curves. RESULTS: The risk of stent thrombosis was higher in the group of patients with impaired clopidogrel response for either cutoff value (for >354 AU x min - HR 12.33; 95% CI 2.49–61.1; P = 0.002). Cardiovascular mortality was also higher in the impaired clopidogrel response group (for >354 AU x min - HR 10.58; 95% CI 2.05–54.58; P = 0.005). We did not find a clear relation of increased clopidogrel response to the risk of bleeding. CONCLUSIONS: The results of this study show that in diabetic ACS patient group treated with PCI an impaired platelet response to clopidogrel measured by the Multiplate analyzer results in increased risk of stent thrombosis and cardiac death

Embankment on Vertical Drains - Pore Pressures During Construction

Excess pore pressures and consolidation settlements observed during the construction of a trial embankment placed on four different types of vertical drains are examined with the aim of evaluating: undrained pore pressure response, field coefficient of consolidation and drain performance

Continuous-variable Werner state: separability, nonlocality, squeezing and teleportation

We investigate the separability, nonlocality and squeezing of continuous-variable analogue of the Werner state: a mixture of pure two-mode squeezed vacuum state with local thermal radiations. Utilizing this Werner state, coherent-state teleportation in Braunstein-Kimble setup is discussed.Comment: 7 pages, 4 figure

Optimal Non-Universally Covariant Cloning

We consider non-universal cloning maps, namely cloning transformations which are covariant under a proper subgroup G of the universal unitary group U(d), where d is the dimension of the Hilbert space H of the system to be cloned. We give a general method for optimizing cloning for any cost-function. Examples of applications are given for the phase-covariant cloning (cloning of equatorial qubits) and for the Weyl-Heisenberg group (cloning of "continuous variables").Comment: 6 page

CHD pile performance, part II:Numerical modelling

In this paper, a set of simple modelling procedures are presented that can be used to estimate the load-settlement behaviour of Continuous Helical Displacement (CHD) piles in sands, in conjunction with the Finite Element Method (FEM). The approach makes use of a stress and strain dependent non-linear soil model that can be parameterised using basic soil data (principally relative density) that can be determined through routine site investigation (e.g. SPT, CPT). The procedures are validated against a database of 1-g physical model tests reported in the Companion Paper, where they are shown to be suitable for estimating the load-settlement behaviour of CHD piles within the serviceability range. In this way they are complimentary to the analytical method for estimating the ultimate capacity of a CHD pile which was developed in the Companion Paper. In the final part of the paper, the FEM and analytical model are applied to four historical field pile load tests on CHD piles conducted at three different sand sites where they are (i) further validated; and (ii) used to discuss potential savings in pile material and therefore cost due to additional confidence in performance determination at both ultimate and serviceability limiting states