Knowledge-Concealing Evidencing of Knowledge About a Quantum State

Area of Science:

• Quantum Information Theory
• Quantum Cryptography
• Relativistic Quantum Information

Background:

• Investigating secure communication protocols in quantum information theory.
• Exploring the limits of zero-knowledge proofs in quantum relativistic settings.
• Addressing the challenge of evidencing knowledge without revealing information.

Purpose of the Study:

• To determine the possibility of zero-knowledge evidencing of quantum states in relativistic protocols.
• To analyze the soundness and completeness of such protocols.
• To propose and evaluate a novel quantum relativistic protocol for secure knowledge evidencing.

Main Methods:

• Theoretical analysis of quantum relativistic protocols.
• Extending previous impossibility results in quantum information theory.
• Developing and analyzing a new quantum relativistic protocol for large dimension 'd'.

Main Results:

• Proved the impossibility of zero-knowledge evidencing in quantum relativistic protocols.
• Demonstrated that no such protocol can be simultaneously sound and complete.
• Presented a new protocol conjectured to be near-optimal in security against Alice.

Conclusions:

• Zero-knowledge evidencing of uniformly distributed quantum states is not achievable in relativistic protocols.
• Existing protocols face limitations in achieving both soundness and completeness.
• The proposed protocol offers a potential solution for secure knowledge evidencing with minimal information leakage.