Boolean games played in a triangle using bi-partite and tri-partite entanglement
Sánchez Muñoz, Victoria
Sánchez Muñoz, Victoria
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Publication Date
2024-04-17
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Thesis
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Abstract
This dissertation analyses the Nash equilibrium points in a triangle network when the three nodes/players are playing pairwise boolean games using bi-partite and tri partite entanglement. The players are given one bit as input and must output another bit; the boolean games are defined by choosing two boolean functions of two variables, one function for the input bits and another for the outputs. The players win jointly each of the games if the function of the inputs matches the function of the outputs. The players also share a 6-qubit quantum state, each owning two qubits, which will be used to play the games, i.e. to decide on their outputs given their inputs by measuring locally their two qubits. This 6-qubit state corresponds either to two GHZ-like quantum states (tri-partite entanglement) or three Bell-like quantum states (bi-partite entanglement). The aim is to compare the performance in terms of the (new) Nash equilibrium points of these two types of quantum resources in the described triangle-network situation for any choice of the two boolean functions defining the game. This research, that mixes quantum games, quantum networks, and quantum resources, presents an interesting and rather rich situation, with potential applications in quantum information, for example, in the quantum internet.
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NUI Galway