Qubit portrait of the photon-number tomogram and separability of two-mode light states

In view of the photon-number tomograms of two-mode light states, using the qubit-portrait method for studying the probability distributions with infinite outputs, the separability and entanglement detection of the states are studied. Examples of entangled Gaussian state and Schr\"{o}dinger cat state are discussed.Comment: 20 pages, 6 figures, TeX file, to appear in Journal of Russian Laser Researc

Inverse spin-s portrait and representation of qudit states by single probability vectors

Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j+1)(4j+1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere. Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits (j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and (2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.Comment: 23 pages, 4 figures, PDF LaTeX, submitted to the Journal of Russian Laser Researc

MuSR method and tomographic probability representation of spin states

Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. Time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. Entanglement phenomenon of a bipartite muon-electron system is investigated via tomographic analogues of Bell number and positive partial transpose (PPT) criterion. Reconstruction of the muon-electron spin state as well as the total spin tomography of composed system is discussed.Comment: 20 pages, 4 figures, LaTeX, submitted to Journal of Russian Laser Researc

Germination and allometry of the native palm tree Euterpe edulis compared to the introduced E. oleracea and their hybrids in Atlantic rainforest

Palms are distinctive plants of tropics and have peculiar allometric relations. Understanding such relations is useful in the case of introduced species because their ability to establish and invade must be clarified in terms of their responses in the new site. Our purpose was to assess the survival and invasive capacity of an introduced palm species in the Atlantic rainforest, Euterpe oleracea Mart., compared to the native Euterpe edulis Mart. and to the hybrids produced between the two species. Considering this, we compared the allometry in different ontogenetic stages, the germination rates, and aspects of the initial development. The ontogenetic stages proposed for both Euterpe illustrated the growth patterns described for palm trees. E. oleracea and hybrids adjusted to the geometric similarity allometric model, while E. edulis presented a slope greater than would be expected considering this model, indicating a greater height for a given diameter. E. oleracea showed the same amount of pulp per fruit as E. edulis and a similar initial development of seedlings. The main differences observed were a lower germination rate and a faster height gain of E. oleracea seedlings. We conclude that E. oleracea, which is similar to E. edulis in aspects of allometry, development, seed and seedling morphology, may be an important competitor of this native palm tree in the Atlantic Forest