A Proposal for Quantum Key Distribution using Quantum Games

Walter O. Krawec, Fei Miao

Luis Fernando Quezada, Shi‐Hai Dong

Abstract This work illustrates a possible application of quantum game theory to the area of quantum information, in particular to quantum cryptography. The study proposed two quantum key‐distribution (QKD) protocols based on the quantum version of the Monty Hall game devised by Flitney and Abbott. Unlike most QKD protocols, in which the bits from which the key is going to be extracted are encoded in a basis choice (as in BB84), these are encoded in an operation choice. The first proposed protocol uses qutrits to describe the state of the system and the same game operators proposed by Flitney and Abbott. The motivation behind the second proposal is to simplify a possible physical implementation by adapting the formalism of the qutrit protocol to use qubits and simple logical quantum gates. In both protocols, the security relies on the violation of a Bell‐type inequality, for two qutrits and for six qubits in each case. Results show a higher ratio of violation than the E91 protocol.

Norihito Toyota

We study a new QKD that is different from the scheme proposed by \cite{Ramz2}, though it essentially takes our ground on three-player quantum games and Greenberg-Horne-Zeilinger triplet entangled state (GHZ state) \cite{Gree} is used. In the scheme proposed in this paper, players in the game, Bob and Charlie (and Alice also) can get some common key or information (applied strategies and their payoffs in the game), when Alice informs Bob and Charlie about some results of the measurement made by her. Even if somebody else knows the public information, he/she can not get any key information. There is not any arbiter in our scheme, since existence of an arbiter increases the risk of wiretapping. Lastly we discuss robustness of the proposed QKD method for eavesdrop. We show that though maximally entangled case and non-entangled case essentially provide an equivalent way as QKD, the latter is not available in the case where there are some eavesdroppers. At the same time, we point put that the entanglement of the initial state is crucial when a partially entangled state is used.

Hong Mei Guo, Juheng Zhang, Gary J. Kœhler

Venugopal S, Kunwar Singh

In the Quantum Computing field, the CHSH (Clauser-Horne-Shimony-Holt) game plays a vital role in determining whether a system is in classical or quantum domain. This quantum advantage property is applied in determining the security of the quantum systems, especially in quantum cryptography, in the form of Device-Independent (DI) secure Quantum Key Distribution (QKD). The traditional CHSH game is designed for a system with two players, where each player has access to one entangled qubit from the Bell’s state. In 2024, Hamza Jaffali and Frédéric Holweck proposed a new three-qubit CHSH game by extending the traditional CHSH game to three players using the three-qubit Greenberger–Horne–Zeilinger (GHZ) state and W state.In this paper, first, we present our findings of new CHSH quantum games with quantum advantage in the four-qubit and five-qubit systems. These CHSH quantum games, when played using their quantum strategy, are found to outperform any classical strategy. Second, we apply the quantum advantage property of the existing three-qubit game to develop the corresponding three party DIQKD protocol. Third, we then apply the quantum advantage property of the newly developed four-qubit and five-qubit games to develop their corresponding four party and five party DIQKD protocols.

Vladimir G. Ivancevic, Tijana T. Ivancevic