A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices

e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible quantum phase transitions. For two of the models, the interactions are three-body and for one the interaction is two-bodyComment: 17 pages, 3 figure

The problem of collecting different body fluids from drivers in the surveys

Objectives: It is not easy to obtain a blood sample from drivers at the roadside for use in epidemiological studies. Therefore, use of saliva samples has become popular. On the other hand, in studies in injured drivers, obtaining a saliva sample can be problematic, e.g. because of injuries. When drug concentrations in blood and saliva need to be compared e.g. in risk calculations, results from different matrices need to be comparable. Because of the different recoveries with saliva collection devices, saliva:blood ratios should be determined for each collection device. Methods: Drug concentrations in blood and saliva samples from different studies (Rosita-2, roadside surveys) were analysed by GC-MS and UPLC-MS/MS and the results were compared for different drugs. Results: While for some drugs like diazepam, relatively good correlation can be observed (r2 = 0.98, n=23, Saliva blood ratio 0.033), for most other drugs there is a very wide scatter when comparing saliva and blood concentrations. These findings confirm those of other published studies. One of the possible explanations is the trapping of basic drugs in saliva because of the pH effects. Conclusion: The correlation between drug concentrations in saliva and whole blood is poor for most drugs. It might be advisable to use whole blood also in a roadside surveys

Comparison of the concentrations of drugs in saliva collected by two sampling methods (Varian® OraLab and Statsure® Saliva Sampler)

Objective: To determine the influence of saliva sampling methods on drug concentrations. Methods: Saliva was obtained from 249 subjects (who had given informed consent) by Varian OraLab and Statsure Saliva?Sampler. OraLab consists of foam-tipped saliva collector. The sponge contains an acid that stimulates salivation. Statsure consists of a collector with a blue indication when 1ml of saliva is collected. After sampling, the collector is transferred to a tube that contains 1ml of buffer. Saliva was analysed with UPLC-MSMS. Results: For all the drugs, the concentrations in the saliva collected with OraLab are 50-70% compared to Statsure, except for morphine (80%) and codeine (92%). Possible explanations are: a buffer could explain a better extraction recovery with Statsure (particularly THC); the stimulation of salivation by an acid in OraLab could also explain the lower concentrations. Conclusions: The correlation coefficients are relatively low (0.61-0.90). For all drugs, the concentrations measured in the saliva collected by OraLab are lower. This could have consequences for the determination of legal cut-offs

A comparison of the entanglement measures negativity and concurrence

In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always larger then $\sqrt{(1-C)^2+C^2}-(1-C)$ where $C$ is the concurrence of the state. Furthermore we derive an explicit expression for the states for which the upper or lower bound is satisfied. Finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared

On the geometry of entangled states

The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert Schmidt distance. While this problem is in general very hard, we show that the following strongly related problem can be solved: find the Hilbert Schmidt distance of an entangled state to the set of all partially transposed states. We prove that this latter distance can be expressed as a function of the negative eigenvalues of the partial transpose of the entangled state, and show how it is related to the distance of a state to the set of positive partially transposed states (PPT-states). We illustrate this by calculating the closest biseparable state to the W-state, and give a simple and very general proof for the fact that the set of W-type states is not of measure zero. Next we show that all surfaces with states whose partial transposes have constant minimal negative eigenvalue are similar to the boundary of PPT states. We illustrate this with some examples on bipartite qubit states, where contours of constant negativity are plotted on two-dimensional intersections of the complete state space.Comment: submitted to Journal of Modern Optic