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

Synthesis of Water Soluble Quantum Dots and their Application for Enzymatic Activity Measurements

Luminescenct Quantum Dots (QDs) intrigue the interest of researchers with their properties of high quantum yield, broad absorption and narrow emission spectra. Since prepared in organic solvents, QDs are not suitable for biological systems. In my study, several methods of cap exchange were tested to enable forming water-soluble QDs with minimal aggregation .The QD-mercaptoacetic acid is simple to synthesize and has good water-solubility, but the QDs are not stable. The direct attachment of peptide molecules to the QDs can passivate the surface and enable water solubility of QDs. It is only applicable for phytochelatin-related peptides, not for all kind of peptides. The co-coupling peptide and PEG on QDs, has good water-solubility when the quantity of PEG and coupling agent EDAC are controlled. The enzymatic activities based on QDs FRET system at different environments was demonstrated and the results show that pH affect the enzymatic activity significantly