Detail publikace

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

ERYGANOV, I. HRDINA, J. NÁVRAT, A.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

quantum games; cooperative games; quantum computing; shapley value; quantum register algebra

Autoři

ERYGANOV, I.; HRDINA, J.; NÁVRAT, A.

Vydáno

1. 10. 2024

Nakladatel

IOP Publishing Ltd

Místo

BRISTOL

ISSN

1751-8121

Periodikum

Journal of Physics A: Mathematical and Theoretical

Ročník

57

Číslo

42

Stát

Spojené království Velké Británie a Severního Irska

Strany od

1

Strany do

24

Strany počet

24

URL

https://www.google.iopscience.iop.org/article/10.1088/1751-8121/ad7c9c

BibTex

@article{BUT189790,
  author="Ivan {Eryganov} and Jaroslav {Hrdina} and Aleš {Návrat}",
  title="Quantization of two- and three-player cooperative games based on QRA",
  journal="Journal of Physics A: Mathematical and Theoretical",
  year="2024",
  volume="57",
  number="42",
  pages="1--24",
  doi="10.1088/1751-8121/ad7c9c",
  issn="1751-8121",
  url="https://www.google.iopscience.iop.org/article/10.1088/1751-8121/ad7c9c"
}