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:1105.2499 · International Journal of Quantum Information

RELATION BETWEEN INFORMATION AND DISTURBANCE IN QUANTUM KEY DISTRIBUTION PROTOCOL WITH CLASSICAL ALICE

Takayuki Miyadera

Published Aug 26, 2011• 22 citations
arXivHTMLPDF

Abstract

The "semiquantum" key distribution protocol introduced by Zou et al. is examined. The protocol while using two-way quantum communication requires only Bob to be fully quantum. We derive a trade-off inequality between information gained by Eve and the disturbance observed by legitimate users. It guarantees that Eve cannot obtain large information if the disturbance is sufficiently small.

DOI
10.1142/s0219749911008118

Related papers

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

Eavesdropping in Semiquantum Key Distribution Protocol: Classical vs. Hadamard Bob

Arpita Maitra, Goutam Paul

The quantum key distribution protocol with classical Bob, well known as semiquantum key distribution, has been proposed a few years back (Boyer et al., PRL 2007, PRA 2009). In this protocol Alice has the same capability as in the traditional BB84 protocol, but Bob is limited by the constraint that he can measure or prepare qubits only in $\{|0>, |1>\}$ basis and reflect any other qubit (or in other words, let it go undisturbed). In this scheme the qubits travel from Alice to Bob and then again from Bob to Alice. We study an eavesdropping strategy on this scheme that listens to the channel in both the directions. With the same level of disturbance induced in the channel, Eve can be extract more information using our two-way strategy than what can be obtained by the direct application of one-way eavesdropping in case of BB84 protocol. Towards resisting this eavesdropping strategy, we modify the semiquantum scheme by incorporating a Hadamard gate at Bob's end.

•May 12, 2012•0 citations

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

M. Yoshida, Ayumu Nakayama, Jun Cheng

We introduce a quantum key distribution protocol using mean multi-kings' problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users' information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users' systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper's extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.

Entropy•Nov 11, 2020•1 citation

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

Semiquantum key distribution

Michel Boyer, Ran Gelles, Dan Kenigsberg +1 more

Secure key distribution between two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semiquantum key distribution protocol was presented [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint and prove their complete robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above; however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.

arXiv:0812.4835•Physical Review A•Mar 30, 2009•298 citations

QUANTUM KEY DISTRIBUTION WITH LIMITED CLASSICAL BOB

Zhiwei Sun, Ruigang Du, Dongyang Long

Recently, quantum key distribution (QKD) with classical Bob has been suggested and proven completely robust by Boyer et al. [Phys. Rev. Lett.99 (2007) 140501] in which quantum Alice has a fully-fledged quantum power, while classical Bob is restricted to preparing and measuring a particle in the computational basis, reflecting or reordering the particles. In this paper, we describe two related but simpler semi-quantum key distribution protocol that exempts classical Bob from measurement (hereafter called limited classical Bob for convenience) and, prove them completely robust. As limited classical Bob can deterministically prepare the qubits, we exploit this feature to construct a semi-quantum secure direct communication protocol, which is the direct communication of secret messages without first producing a shared secret key.

arXiv:1106.4615•International Journal of Quantum Information•Feb 1, 2013•44 citations
The "semiquantum" key distribution protocol introduced by Zou et al. is examined. The protocol while using two-way quantum communication requires only Bob to be fully quantum. We derive a trade-off inequality between information gained by Eve and the disturbance observed by legitimate users. It guarantees that Eve cannot obtain large information if the disturbance is sufficiently small.
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.
The quantum key distribution protocol with classical Bob, well known as semiquantum key distribution, has been proposed a few years back (Boyer et al., PRL 2007, PRA 2009). In this protocol Alice has the same capability as in the traditional BB84 protocol, but Bob is limited by the constraint that he can measure or prepare qubits only in {∣0>,∣1>}\{|0>, |1>\}{∣0>,∣1>} basis and reflect any other qubit (or in other words, let it go undisturbed). In this scheme the qubits travel from Alice to Bob and then again from Bob to Alice. We study an eavesdropping strategy on this scheme that listens to the channel in both the directions. With the same level of disturbance induced in the channel, Eve can be extract more information using our two-way strategy than what can be obtained by the direct application of one-way eavesdropping in case of BB84 protocol. Towards resisting this eavesdropping strategy, we modify the semiquantum scheme by incorporating a Hadamard gate at Bob's end.
We introduce a quantum key distribution protocol using mean multi-kings' problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users' information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users' systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper's extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.
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.
Secure key distribution between two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semiquantum key distribution protocol was presented [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint and prove their complete robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above; however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.
Recently, quantum key distribution (QKD) with classical Bob has been suggested and proven completely robust by Boyer et al. [Phys. Rev. Lett.99 (2007) 140501] in which quantum Alice has a fully-fledged quantum power, while classical Bob is restricted to preparing and measuring a particle in the computational basis, reflecting or reordering the particles. In this paper, we describe two related but simpler semi-quantum key distribution protocol that exempts classical Bob from measurement (hereafter called limited classical Bob for convenience) and, prove them completely robust. As limited classical Bob can deterministically prepare the qubits, we exploit this feature to construct a semi-quantum secure direct communication protocol, which is the direct communication of secret messages without first producing a shared secret key.