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Quantum Information and Computation

Quantum solution to a three player Kolkata restaurant problem using entangled qutrits

SharifPuya, HeydariHoshang

Published Mar 1, 2014• 0 citations
Publisher

Abstract

Three player quantum Kolkata restaurant problem is modelled using three entangled qutrits. This first use of three level quantum states in this context is a step towards a N-choice generalization o...
DOI
10.5555/2600508.2600514

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Three player quantum Kolkata restaurant problem is modelled using three entangled qutrits. This first use of three level quantum states in this context is a step towards a NNN-choice generalization of the NNN-player quantum minority game. It is shown that a better than classical payoff is achieved by a Nash equilibrium solution where the space of available strategies is spanned by subsets of SU(3) and the players share a tripartite entangled initial state.
The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.
We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by a n-player generalization trough the quantum minority games, and finishing with a contribution towards a n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as an introduction suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.