Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.Comment: 5 pages and 3 figure

Cyclolinopeptides in flaxseed and flaxseed products

Cyclolinopeptides (CLPs), a group of naturally occurring, hydrophobic, cyclic peptides in flax, have attracted a great deal of attention due to their immunosuppressive activity. The purpose of this project was to increase our understanding of the occurrence of CLPs in flaxseed, flaxseed tissues and flaxseed products. In the first study, systematic methods for CLP extraction, isolation, detection and quantification were developed. The solubility of CLPs in acetone led to its use as a preferred solvent for extraction of CLPs and other hydrophobic compounds from whole flaxseed. Solid phase extraction with a silica gel column followed by selective elution with organic solvents of increasing polarity enabled the isolation of a crude peptide-rich fraction. Reverse phase HPLC chromatography of peptide-rich fractions provided a method for separation and quantification of CLPs. In the second study, the levels of CLPs in cultivars of flaxseed were studied to determine if there was any impact of flax genotype or environment on peptide levels. The concentration of total CLPs varied from 189 µg/g (Flanders) to 303 µg/g (Somme) in the cultivars tested. Environment, cultivar and their interaction affected the observed concentration of CLPs. In the third study, the concentrations of CLPs in fractions produced from flaxseed were measured by HPLC in seed coat, cotyledon and oil bodies. The concentration of CLPs was higher in the cotyledon than in the seed coat. The highest CLP concentrations were found in the oil bodies. In the fourth study, CLP levels in flaxseed oil were measured during and after oil extraction and refining. The concentration of CLPs was higher in expeller-extracted crude oil and solid foots and lower in flaxseed meal. A comparison of CLP levels in flaxseed oil extracted with a small expeller and in commercially-produced flaxseed oil was performed. Crude flaxseed oil produced with a small expeller had higher levels of peptides than were observed in commercial flaxseed oil available at a local retail health food store. The effect of oil refining processes, including acid degumming and alkali refining on CLP stability, was studied. Acid degumming using 1% H3PO4 effectively removed all CLPs. Alkali refining was also demonstrated as being effective at decreasing levels of CLPs, although it failed to remove all peptides

Complete hyperentangled-Bell-state analysis for quantum communication

It is impossible to unambiguously distinguish the four Bell states in polarization, resorting to linear optical elements only. Recently, the hyperentangled Bell state, the simultaneous entanglement in more than one degree of freedom, has been used to assist in the complete Bell-state analysis of the four Bell states. However, if the additional degree of freedom is qubitlike, one can only distinguish 7 from the group of 16 states. Here we present a way to distinguish the hyperentangled Bell states completely with the help of cross-Kerr nonlinearity. Also, we discuss its application in the quantum teleportation of a particle in an unknown state in two different degrees of freedom and in the entanglement swapping of hyperentangled states. These applications will increase the channel capacity of long-distance quantum communication.Comment: 9 pages, 6 figure