Separability in 2xN composite quantum systems

We analyze the separability properties of density operators supported on \C^2\otimes \C^N whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states have rank larger than N. We also give a separability criterion for a generic density operator such that the sum of its rank and the one of its partial transpose does not exceed 3N. If it exceeds this number we show that one can subtract product vectors until decreasing it to 3N, while keeping the positivity of $\rho$ and its partial transpose. This automatically gives us a sufficient criterion for separability for general density operators. We also prove that all density operators that remain invariant after partial transposition with respect to the first system are separable.Comment: Extended version of quant-ph/9903012 with new results. 11 page

Separable approximations of density matrices of composite quantum systems

We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)]. Such approximations allow to represent in an optimal way any density operator as a sum of a separable state and an entangled state of a certain form. For two qubit systems (M=N=2) the best separable approximation has a form of a mixture of a separable state and a projector onto a pure entangled state. We formulate a necessary condition that the pure state in the best separable approximation is not maximally entangled. We demonstrate that the weight of the entangled state in the best separable approximation in arbitrary dimensions provides a good entanglement measure. We prove in general for arbitrary M and N that the best separable approximation corresponds to a mixture of a separable and an entangled state which are both unique. We develop also a theory of optimal separable approximations for states with positive partial transpose (PPT states). Such approximations allow to decompose any density operator with positive partial transpose as a sum of a separable state and an entangled PPT state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure

Separability and entanglement in 2x2xN composite quantum systems

We investigate separability and entanglement of mixed states in ${\cal C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For the 3 qubit case (N=2) we prove that all states $\rho$ that have positive partial transposes and rank 3 are separable. We provide also constructive separability checks for the states $\rho$ that have the sum of the rank of $\rho$ and the ranks of partial transposes with respect to all subsystems smaller than 15N-1.Comment: Finally corrected file submitted. Numerous misprints and small errors corrected, better versions of constructive separability checks included, updated and extended reference

Synchrotron radiation-based experimental determination of the optimal energy for cell radiotoxicity enhancement following photoelectric effect on stable iodinated compounds

This study was designed to experimentally evaluate the optimal X-ray energy for increasing the radiation energy absorbed in tumours loaded with iodinated compounds, using the photoelectric effect. SQ20B human cells were irradiated with synchrotron monochromatic beam tuned at 32.8, 33.5, 50 and 70 keV. Two cell treatments were compared to the control: cells suspended in 10 mg ml1 of iodine radiological contrast agent or cells pre-exposed with 10 mM of iodo-desoxyuridine (IUdR) for 48 h. Our radiobiological end point was clonogenic cell survival. Cells irradiated with both iodine compounds exhibited a radiation sensitisation enhancement. Moreover, it was energy dependent, with a maximum at 50 keV. At this energy, the sensitisation calculated at 10% survival was equal to 2.03 for cells suspended in iodinated contrast agent and 2.60 for IUdR. Cells pretreated with IUdR had higher sensitisation factors over the energy range than for those suspended in iodine contrast agent. Also, their survival curves presented no shoulder, suggesting complex lethal damages from Auger electrons. Our results confirm the existence of the 50 keV energy optimum for a binary therapeutic irradiation based on the presence of stable iodine in tumours and an external irradiation. Monochromatic synchrotron radiotherapy concept is hence proposed for increasing the differential effect between healthy and cancerous tissue irradiation

Piétons jeunes, piétons âgés et accidentabilité

The authors analysed 454 pedestrian accidents that occurred in a civil parish of Brussels. The study is based on a Benzecri analysis of the correspondence between individual characteristics and environmental characteristics. The analysis reveals three principal types of pedestrian involved in an accident and three principal types of environment.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Comparison of soil tillage systems in the cereal crop rotation

Соответствующие полевые опыты проводились в период 1972-1981 гг. в опытной станции Липки, в 4-польном севообороте: 1 - картофель, 2 - яровой ячмень, 3 - овес, 4 - рожь. Сравнивали 4 системы обработки: 1 - типичную плужную обработку, 2, 3, 4 - упрощенные виды обработки при двух уровнях минерального удобрения: 1 NPK и 1,5 NPK. Более мелкая вспашка и применение культиватора, дисковой бороны и почвофрезы (2, 3, 4) в сравнении с типичной плужной обработкой (1) в период роста возделываемых культур повышали на 9-51% связность почвы и запас воды в слое 0-25 см, преимущественно в период роста овса и ржи. Сравниваемые системы обработки почвы не оказывали существенного влияния на плотность почвы. Дифференциация глубины вспашки под картофель и упрощенная обработка под зерновые не оказывали существенного влияния на урожаи возделываемых культур. Под влиянием повышенного уровня удобрения (1,5 NPK) существенно повышались только урожаи картофеля.The respective field experiment was carried out in the period 1972-1981 at the Agricultural Experiment Station Lipki within the 4-field crop rotation: 1 - potatoes, 2 - summer barley, 3 - oats, 4 - rye. Four soil tillage systems were compared, viz.: 1 - typical ploughing, 2, 3, 4 - simplified tillage measures at mineral fertilization levels: 1 NPK and 1,5 NPK. Shallowing of the plough tillage and application of cultivator, disc harrow and rotovator (2. 3,4) as compared to typical ploughing (1) during the growth of crops resulted in an increase by 9-51% the soil compactness in the 0-25 cm layer, mainly during the growth of oats and rye. The soil tillage systems compared did not exert any significant effect on yielding of the above crops. The increased fertilization level (1.5 NPK) led to a significant growth of potato yields only

Contributions of personal, psychological and organisational factors to the understanding of Upper Limb Disorders (ULD) ’s developments :presentation of the research design.

info:eu-repo/semantics/publishe

Effect of soil tillage and fertilization on yielding and weediness of crops in a cereal crop rotation

В 10-летнем (1972-1982) полевом опыте проводимом в опытной станции Липки сравнивали следующие факторы: I - две глубины вспашки под картофель, 25 и 35 см, II - четыре способа обработки почвы на разную глубину под зерновые культуры, III - два уровня минерального удобрения: 1 NPK - 260 кг/га под картофель и 200 кг/га под зерновые и 1,5 NPK - 390 кг/га под картофель и 300 кг/га под зерновые. Они проводились в 4-полевом севообороте: 1 - картофель, 2 - яровой ячмень, 3 - овес и 4. озимая рожь. Сравниваемые способы и глубины обработки почвы не дифференцировали урожаев возделываемых культур, тогда как повышенное на 50% удобрение NPK повышало урожаи зерновых на 5-9%, а картофеля на 12%, Более мелкая обработка почвы, особенно активными орудиями, повышала засоренность зерновых на 20-50%, а повышенное минеральное удобрение NPK сокращало ее только в зерновых на 3-14%. Самая большая масса сррняков была в озимой ржи, в которой наблюдалась компенсация Арега spica-venti. Под влиянием упрощений в обработке почвы заметно повышалось участие Agropyron repens. Не установлено зависимости между засоренностью и урожайностью растений.In the 10-year field experiment (1972-1982) carried out at the Agricultural Experiment Station Lipki, the following factors were compared: I - two ploughing depths for potatoes, 25 and 35 cm, II - four soil tillage ways of different depth for successive cereal crops, III - two mineral fertilization levels: 1 NPK 260 kg/ha for potatoes and 200 kg/ha for cereals as well as 1.5 NPK - 390 kg/ha for potatoes and 300 kg/ha for cereals in a 4-field crop rotationr 1 - potatoes, 2 - summer barley, 3 - oats, 4 - winter rye. The way and depths of soil tillage compared did not differentiate the yields of crops, whereas the NPK fertilization level increased by 50% resulted in yield increments of cereals by 5-9% and of potatoes by 12%. Shallowing of the soil tillage, particularly when applied with active tools, resulted in an increased weediness of cereals by 20-50%, whereas increased NPK fertilization level reduced it only in cereals by 3-13%. The greatest mass of weeds has been found in winter rye, where compensation of Apera spica-venti was observed. Simplifications of the soil tillage led to a distinct increase of the share of Agropyron repens. No relationship between weediness and yielding of plants has been found