Boolean games played in a triangle using bi-partite and tri-partite entanglement
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Date
2024-04-17Author
Sánchez Muñoz, Victoria
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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.