Strategic Insights From Playing the Quantum Tic-Tac-Toe

In this paper, we perform a minimalistic quantization of the classical game of tic-tac-toe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. We also admit interference effects, by squaring the sum of amplitudes over all moves by a player to compute his or her occupation level of a given site. A player wins when the sums of occupations along any of the eight straight lines we can draw in the $3 \times 3$ grid is greater than three. We play the quantum tic-tac-toe first randomly, and then deterministically, to explore the impact different opening moves, end games, and different combinations of offensive and defensive strategies have on the outcome of the game. In contrast to the classical tic-tac-toe, the deterministic quantum game does not always end in a draw. In contrast also to most classical two-player games of no chance, it is possible for Player 2 to win. More interestingly, we find that Player 1 enjoys an overwhelming quantum advantage when he opens with a quantum move, but loses this advantage when he opens with a classical move. We also find the quantum blocking move, which consists of a weighted superposition of moves that the opponent could use to win the game, to be very effective in denying the opponent his or her victory. We then speculate what implications these results might have on quantum information transfer and portfolio optimization.Comment: 20 pages, 3 figures, and 3 tables. LaTeX 2e using iopart class, and braket, color, graphicx, multirow, subfig, url package

High metabolomic microdiversity within co-occurring isolates of the extremely halophilic bacterium Salinibacter ruber

Salinibacter ruber is an extremely halophilic member of the Bacteroidetes that thrives in crystallizer ponds worldwide. Here, we have analyzed two sets of 22 and 35 co-occurring S. ruber strains, newly isolated respectively, from 100 microliters water samples from crystalizer ponds in Santa Pola and Mallorca, located in coastal and inland Mediterranean Spain and 350 km apart from each other. A set of old strains isolated from the same setting were included in the analysis. Genomic and taxonomy relatedness of the strains were analyzed by means of PFGE and MALDI-TOF, respectively, while their metabolomic potential was explored with high resolution ion cyclotron resonance Fourier transform mass spectrometry (ICR-FT/MS). Overall our results show a phylogenetically very homogeneous species expressing a very diverse metabolomic pool. The combination of MALDI-TOF and PFGE provides, for the newly isolated strains, the same scenario presented by the previous studies of intra-specific diversity of S. ruber using a more restricted number of strains: the species seems to be very homogeneous at the ribosomal level while the genomic diversity encountered was rather high since no identical genome patterns could be retrieved from each of the samples. The high analytical mass resolution of ICR-FT/MS enabled the description of thousands of putative metabolites from which to date only few can be annotated in databases. Some metabolomic differences, mainly related to lipid metabolism and antibiotic-related compounds, provided enough specificity to delineate different clusters within the co-occurring strains. In addition, metabolomic differences were found between old and new strains isolated from the same ponds that could be related to extended exposure to laboratory conditions.This work was supported by the projects CLG2009-12651-C02-01 and 02; and CE-CSD2007-0005 of the Spanish Ministry of Science and Innovation, and all three projects were also co-financed with FEDER support from the European Union. JBE was financed by the Government of the Balearic Islands, Ministry of Economy and Finances