Quantization of two- and three-player cooperative games based on QRA

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F24%3APU152291" target="_blank" >RIV/00216305:26210/24:PU152291 - isvavai.cz</a>
Result on the web
<a href="https://www.google.iopscience.iop.org/article/10.1088/1751-8121/ad7c9c" target="_blank" >https://www.google.iopscience.iop.org/article/10.1088/1751-8121/ad7c9c</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ad7c9c" target="_blank" >10.1088/1751-8121/ad7c9c</a>

Result language
angličtina
Original language name
Quantization of two- and three-player cooperative games based on QRA
Original language description
In this paper, a novel quantization scheme for cooperative games is proposed. The circuit is inspired by the Eisert-Wilkens-Lewenstein protocol, which was modified to represent cooperation between players and extended to 3-qubit states. The framework of Clifford algebra is used to perform necessary computations. In particular, we use a direct analogy between Dirac formalism and Quantum Register Algebra (QRA) to represent circuits. This analogy enables us to perform automated proofs of the circuit equivalence in a simple fashion. The expected value of the Shapley value concerning quantum probabilities is employed to distribute players' payoffs after the measurement. We study how entanglement, representing the level of pre-agreement between players, affects the final utility distribution. The paper also demonstrates how the QRA and GAALOP software can automate all necessary calculations.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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