Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0104016 · Physical Review A

Quantum key distribution betweenNpartners: Optimal eavesdropping and Bell’s inequalities

Valerio Scarani, Nicolas Gisin

Published Dec 12, 2001• 63 citations
arXivHTMLPDF

Abstract

Quantum secret-sharing protocols involving N partners are key distribution protocols in which Alice encodes her key into $N\ensuremath{-}1$ qubits, in such a way that all the other partners must cooperate in order to retrieve the key. On these protocols, several eavesdropping scenarios are possible: some partners may want to reconstruct the key without the help of the other ones, and consequently collaborate with an Eve that eavesdrops on the other partners' channels. For each of these scenarios, we give the optimal individual attack that Eve can perform. A link with Bell's inequality is demonstrated analytically for half of the scenarios, and is conjectured on the basis of numerical estimates for the other scenarios: the authorized partners have a higher information on the key than the unauthorized ones if and only if they can violate a Bell's inequality.

DOI
10.1103/physreva.65.012311

Related papers

N-partners Quantum Communication and Bell's inequalities

Valerio Scarani, Nicolas Gisin

We present strong evidences for the existence of a link between the security of quantum communication protocols involving N partners and the violation of some Bell's inequalities. The link allows to establish optimal eavesdropping strategies for all N; in particular, we discuss eavesdropping on quantum secret sharing (N=3). The arguments are independent of the local hidden variable debate.

•Jan 23, 2001•1 citation

New approach to quantum key distribution via quantum encryption

A. Fahmi

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.

arXiv:quant-ph/0604185•Quantum Information and Computation•Sep 1, 2009•0 citations

BELL'S INEQUALITIES DETECT EFFICIENT ENTANGLEMENT

Antonio Acín, Nicolas Gisin, Lluís Masanes +1 more

We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a family of attacks of two qubits, acting on half of a maximally entangled state of two qubits, the violation of a Bell inequality implies the possibility of an efficient secret-key extraction.

arXiv:quant-ph/0310166•International Journal of Quantum Information•Mar 1, 2004•38 citations

QUANTUM KEY DISTRIBUTION WITH CLASSICAL ALICE

Hua Lu, Qing-yu Cai

It seems that quantum key distribution (QKD) may be completely insecure when the message sender Alice always encodes her key bits in a fixed basis. In this paper, we present a QKD protocol with classical Alice, i.e. Alice always encodes her key bit in the {|0〉,|1〉} basis (we call it classical {0,1} basis) and the eavesdropper Eve knows this fact. We prove that our protocol is completely robust against any eavesdropping attack and present the amount of tolerable noise against Eve's individual attack. Next, we present a QKD protocol to demonstrate that secure key bits can be distributed even if neither Alice nor Bob has quantum capacities, and extend this idea to a QKD network protocol with numerous parties who have only classical capacities. Finally, we discuss that quantum is necessary in QKD for security reasons, but both Alice and Bob may be classical.

International Journal of Quantum Information•Dec 1, 2008•70 citations

OPTIMAL EAVESDROPPING ON NOISY STATES IN QUANTUM KEY DISTRIBUTION

Z. SHADMAN, H. KAMPERMANN, T. MEYER +1 more

We study eavesdropping in quantum key distribution with the six state protocol, when the signal states are mixed with white noise. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or in a realistic scenario where Eve cannot replace the noisy quantum channel by a noiseless one. We find Eve's optimal mutual information with Alice, for individual attacks, as a function of the qubit error rate. Our result is that added quantum noise reduces Eve's mutual information more than Bob's.

arXiv:0804.0587•International Journal of Quantum Information•Feb 1, 2009•20 citations

On the security of the quantum key distribution using the Mean King Problem

M. Yoshida, Takayuki Miyadera, Hideki Imai

It is anticipated that quantum key distribution enable us to share a secret key while guaranteeing unconditionally security. In this paper, we discuss the quantum key distribution using the Mean King Problem which was proposed by J. Bub in 2001. While this two-way quantum protocol is essentially different from the other one-way protocols like the BB84, it has been shown that Eve cannot gain any information without being detected even in this protocol. Assuming two attack scenarios in this protocol, we derive two trade-off inequalities showing that the larger Eve's information gain is, the higher the detectability becomes. These quantitative inequalities enables the legitimate users to estimate Eve's information gain.

International Symposium on Information Theory and its Applications•Oct 1, 2010•4 citations
Quantum secret-sharing protocols involving N partners are key distribution protocols in which Alice encodes her key into N\ensuremath−1N\ensuremath{-}1N\ensuremath−1 qubits, in such a way that all the other partners must cooperate in order to retrieve the key. On these protocols, several eavesdropping scenarios are possible: some partners may want to reconstruct the key without the help of the other ones, and consequently collaborate with an Eve that eavesdrops on the other partners' channels. For each of these scenarios, we give the optimal individual attack that Eve can perform. A link with Bell's inequality is demonstrated analytically for half of the scenarios, and is conjectured on the basis of numerical estimates for the other scenarios: the authorized partners have a higher information on the key than the unauthorized ones if and only if they can violate a Bell's inequality.
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.
It seems that quantum key distribution (QKD) may be completely insecure when the message sender Alice always encodes her key bits in a fixed basis. In this paper, we present a QKD protocol with classical Alice, i.e. Alice always encodes her key bit in the {|0〉,|1〉} basis (we call it classical {0,1} basis) and the eavesdropper Eve knows this fact. We prove that our protocol is completely robust against any eavesdropping attack and present the amount of tolerable noise against Eve's individual attack. Next, we present a QKD protocol to demonstrate that secure key bits can be distributed even if neither Alice nor Bob has quantum capacities, and extend this idea to a QKD network protocol with numerous parties who have only classical capacities. Finally, we discuss that quantum is necessary in QKD for security reasons, but both Alice and Bob may be classical.
We study eavesdropping in quantum key distribution with the six state protocol, when the signal states are mixed with white noise. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or in a realistic scenario where Eve cannot replace the noisy quantum channel by a noiseless one. We find Eve's optimal mutual information with Alice, for individual attacks, as a function of the qubit error rate. Our result is that added quantum noise reduces Eve's mutual information more than Bob's.
It is anticipated that quantum key distribution enable us to share a secret key while guaranteeing unconditionally security. In this paper, we discuss the quantum key distribution using the Mean King Problem which was proposed by J. Bub in 2001. While this two-way quantum protocol is essentially different from the other one-way protocols like the BB84, it has been shown that Eve cannot gain any information without being detected even in this protocol. Assuming two attack scenarios in this protocol, we derive two trade-off inequalities showing that the larger Eve's information gain is, the higher the detectability becomes. These quantitative inequalities enables the legitimate users to estimate Eve's information gain.