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arXiv:2308.09194

Quantum Key Distribution using Expectation Values of Super-classical GHZ States

Hyung Sup Choi, Ye Jin Han, collin kessinger, Qiaoren Wang

Published Aug 17, 2023• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2308.09194

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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.
In order to improve the efficiency of deterministic key distribution,a quantum key distribution scheme based on GHZ states entanglement swapping was proposed.By sharing a pair of GHZ states between communicators,Bob can deduce deterministic key from classic information which was sent by Alice who took entanglement and measurement operation.Compared with other scheme based on GHZ entanglement state,two GHZ states produced by Bob in the proposed scheme and particles are distributed not by Alice,but Bob.Security analysis results show that any eavesdropper can be found in time.The proposed scheme has high distribution efficiency in that all the GHZ states can be used to transmit information except those chosen for checking eavesdroppers,it can reach the distribution efficiency at 60% and simple to operation.
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 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.
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.
Recently, Zhang, Li and Guo (ZLG) suggested a new approach to quantum key distribution by using a shared Bell state which acts as quantum key in order to encode and decode classical information. Subsequently, others extended ZLG protocol to d-dimensional systems and to quantum secret sharing based on reusable GHZ states. However, Gao et al. have shown that if Eve employs a special strategy to attack, these protocols become insecure. Afterwards, they repair ZLG protocol so that their eavesdropping strategy becomes inefficient. In this paper, we investigate the security of ZLG quantum key distribution protocol and show that it is not secure against Eve's attacks and with probability of one half she gets all of the keys without being detected by the two parties. In this eavesdropping strategy, Eve transforms the previously shared Bell state between Alice and Bob to two Bell states among herself and the parties. Moreover, we briefly show that ZLG's repairing by Gao et al's is not efficient against of our attack and Eve can choose an appropriate rotation angle and measurement bases which help her to do eavesdropping. Afterwards, we discuss generalization of ZLG protocol to d-dimensional systems and show that with probability 1/d, Eve gets all of keys. We show that quantum secret sharing based on reusable GHZ states is also not secure and with probability one half, Eve gets all of keys. We repair them by going to higher dimensional shared EPR or GHZ states. Finally, we compare ZLG protocol with ours and show that the ZLG protocol and its extensions are less robust against the channel noise with respect to ours.
In this paper, we develop, a quantum key distribution protocol based on the Greenberger-Horne-Zeilinger states (GHZs). The particles are exchanged among the users in blocks through two steps. In this protocol, for three-particle GHZs three keys can be simultaneously generated. The advantage of this is that the users can select the most suitable key for communication. The protocol can be generalized to N users to provide N keys. The protocol has two levels for checking the eavesdroppers. Moreover, we discuss the security of the protocol against different attacks.