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Quantum Advantage in Trading: A Game-Theoretic Approach

Norbert M. Linke, Faisal Shah Khan, Dror Baron, Anton T. Than

Published May 9, 2025• 0 citations
Publisher

Abstract

Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.

DOI
10.17615/af1s-7c34

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Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.
Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.
Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.
Game theory is a well established field with applications in many areas including the social sciences, biology, and computer science [6]. Recently, however, researchers in quantum computation have begun to study the implications of games set in the quantum domain (i.e. game theoretical situations where either one or more players have quantum computational power or where the implementation of strategies uses some form of quantum information). Such a setting allows for entanglement and superpositions of strategies and evaluation of payoffs using quantum measurement. This approach to game theory, according to some scholars in the field, could help us understand certain physical systems, improve economic markets, and develop quantum algorithms. I have conducted an investigation into quantum game theory. I have constructed simulation tools using Maple that, along with research into related work, have helped gain some insight into this new field. The important solutions in classical game theory are usually Nash equilibria. What do they look like in the quantum realm? In what
This work is mainly based on quantum game-theoretic techniques and their application to quantum information theory.Quantum game theory is an important development in quantum computation and may have implications for quantum information and quantum communication.The select of quantum memory on quantum games have been studied.Three di􀀞erent games such as, Prisoner Dilemma, Battle of the Sexes and Chicken have been analyzed in the quantum domain. By considering the restricted game \nsituation, it is shown that the ects of quantum memory and decoherence become e􀀞ective in a maximally entangled case.For which the quantum player can out perform the classical player in all the three games. It is also shown that the quantum player enjoys an advantage over the classical player in Battle of the Sexes game for the amplitude-damping and the depolarizing channels.The quantum memory compensates the reduction in player pay is due to decoherence. It has no ect on the Nash equilibria of the three games.A generalization of two-player quantization scheme to a three-player Prisoners Dilemma game under the ect of correlated noise is also presented.In a restricted game scenario, it is shown the quantumplayer is always better; for all values of the decoherence parameter for the entire range of memory parameter.It is seen that for maximum degree of correlation, the game does not become \nnoiseless and quantum player can still outscore the classical players for the entire range of the decoherence parameter producing an interesting result in comparison with a two-player quantum game.It is also shown that correlated noise has not on the Nash equilibrium of the game.By exploiting the three-player quantization scheme, we have studiedthe communication aspects of a three-player Prisoner Dilemma quantum game. It is shown that entanglement plays a dominant role in a three-player quantum game.On the baois of initial state and the measurement basis entanglement parameters, a relation among different pay is established.It is investigated that the strategies of the players act as information carriers in quantum games. A relationship for the information shared among the parties is also established.A scheme for quantum key distribution is proposed in which a secret key can be generated from the data coming through a partially entanglement breaking channel.This scheme is rather deterministic andcient in the sense that two classical bits can be transferred \nper entangled pair of qubits.Furthermore, it is important to point out that, in this scheme, same symbol can be used for Eve detection and key generation. It is also worth noting that the eavesdropper, Eve, can be detected very easily from the disturbance of the elements of the decoding bimatrix. We have checked for the \nsecurity of the scheme and found it secure against individual attacks.It is further investigated that quantum games are useful in developing quantum cryptographic protocols.A multiparty quantum cryptographic protocol using tripartite entangled GHZ states is devised using game-theoretic techniques.In this protocol, two classical bits can be transferred per entangled pair of qubits to the communicating parties.Unitary operators applied by the sender on a tripartite entangled state encodes a classical symbol that can be decoded at receiver end with the help of a decoding matrix. In this protocol, if Eve interferes during the transmission, she can be detected by the disturbance of the decoding matrix. Our security analysis shows that this protocol is also secure against intercept/re-send attacks.
Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilized as a mechanism to witness and determine quantum correlation. By combining quantum theory with Bayesian game theory, a constant-sum game is designed in which the players are competing against each other and crucially gain at the other player’s expense. Subsequently, it is found that mixed strategy Nash equilibria are only necessary when considering quantum correlation for the designed game. This reveals that a Bayesian game-theoretic framework yields a sufficient condition for detecting quantum effects.