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arXiv:1010.1813

Key Distribution based on Three Player Quantum Games

Norihito Toyota

Published Oct 9, 2010• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1010.1813

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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.
We propose a new quantum key distribution scheme that is based on the optimum expectation values of maximally entangled Greenberger-Horne-Zeilinger states. Our protocol makes use of the degrees of freedom in continuously variable angles, thereby increasing the security of the key distribution. Outlined are two protocols that distribute a key from Alice to Bob using the above idea, followed by an extension that allows for the same key to be shared with Charlie. We show how this scheme provides for certain detection of any eavesdropper through absolute violation rather than the probabilistic violation used in many protocols.
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Abstract In this work, a one‐sided measurement‐device‐independent quantum key distribution protocol that uses Bell and Greenberger–Horne–Zeilinger (GHZ) states is proposed. The protocol considers three parties: Alice and Bob, who will share the key at the end of the protocol; and Charlie, who plays the role of facilitating the key distribution without having access to the key itself. Alice and Charlie are trusted users, while Bob is uncharacterized. The protocol is asymmetrical, meaning that Alice sends one qubit while Bob sends two; this allows Bob to identify himself via a previously assigned ID; if this authentication fails, the key distribution also will.
We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different combinations of initial state and measurement basis entanglement parameters. A relation among these different payoffs is also established. We also study the communication aspects of the three-player game. By exploiting different combinations of initial state and measurement basis entanglement parameters, we establish a relationship for the information shared among the parties. It is seen that the strategies of the players act as carriers of information in quantum games.
A novel approach to quantum cryptography to be called NQKD, networking quantum key distribution, has been developed for secure quantum communication schemes on the basis of the complementary relations of entanglement Greenberger–Horne–Zeilinger (GHZ) triplet states. One scheme distributes the private key among legal participants in a probabilistic manner, while another transmits the deterministic message with some certainty. Some decoy photons are employed for preventing a potential eavesdropper from attacking quantum channels. The present schemes are efficient as there exists an elegant method for key distributions. The security of the proposed schemes is exactly guaranteed by the entanglement of the GHZ quantum system, which is illustrated in security analysis.
We propose a quantum key distribution (QKD) scheme in which four parties can simultaneously share a secret key via optical device. The participants divide the communication into two modes, namely, detecting mode and message mode. Taking advantage of controlled secret short key technology, the participants together can achieve the detecting mode or the message mode by switching between their two sets of optical devices. In the detecting mode, the key distributer Alice utilizes a single-photon state resource and two beam splitters and the other three participants Bob, Charlie and Dick use first-type devices to detect the superposition of vacuum and single-particle states. Hence, any eavesdropping can be found by using a variant of Bell's inequality. In the message mode, Alice uses a two-photon Bell-state resource and two polarization beam splitters instead of the single-particle state resource and beam splitters used in the detecting mode and the other three participants use second-type devices to detect photons. In this case, the secret key can be successfully distributed from Alice to the other three ones. Moreover, the present four-party QKD scheme can be generalized to a 2n-party QKD scheme by using n-photon Greenberg–Horne–Zeilinger.