By J. N. Leaw, S. A. Cheong
Abstract:
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.
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This programme explores the complexity and diversity of business in an increasingly interconnected world. Students will engage in critical analysis of international business and investigate the international context of business today. Drawing on current University of Greenwich research and international academic theory, there is a strong emphasis on real-life case studies and professional management application. This MA will help students to develop skills in assessing the global environment for business, identifying new international business opportunities and analysing international markets and industries. The programme provides students who may not have a first degree in business with a grounding in business management, followed by specialised international business courses.