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

Area of Science:

• Quantum Information Science
• Cryptography
• Theoretical Physics

Background:

• Quantum key distribution (QKD) enables secure communication.
• The relationship between information gain and disturbance is crucial for QKD security, as exemplified by the information disturbance theorem in the BB84 protocol.

Purpose of the Study:

• To introduce a novel quantum key distribution protocol utilizing the mean multi-kings problem.
• To analyze the trade-off between an eavesdropper's information gain and the disturbance introduced in the legitimate users' shared secret key.

Main Methods:

• Development of a QKD protocol based on the mean multi-kings problem.
• Mathematical derivation of trade-off inequalities.
• Analysis of a three-party (sender, two receivers) system with an eavesdropper interacting with an ancilla system.

Main Results:

• Derived trade-off inequalities quantifying the relationship between eavesdropper distinguishability and legitimate user error probability.
• Demonstrated that eavesdropper's information extraction inherently disturbs quantum states.
• Showed that increased eavesdropping leads to a higher error probability for the shared secret key.

Conclusions:

• The proposed protocol establishes a clear link between an eavesdropper's ability to gain information and the induced errors in the secret key.
• This work reinforces the fundamental security principles of quantum key distribution, showing that security is intrinsically tied to the disturbance caused by observation.