研究目的

To provide a quantum analogue of Shannon's impossibility result for encryption schemes with imperfect secrecy and imperfect correctness, and to study information-theoretically secure quantum encryption with different secrecy definitions.

研究成果

The paper generalizes Shannon's impossibility to quantum encryption with imperfect secrecy and correctness, showing that a classical key of length at least 2n + log(1 - γ - √(2ε)) is required for n qubits. It also demonstrates that weak information-theoretic security implies stronger security with a loss factor of d2, which is acceptable for small secrecy errors. Applications to existing quantum encryption schemes are discussed, and lower bounds for key length are established for both security notions.

研究不足

The study is theoretical and does not involve practical implementations or experimental validations. The results assume specific error bounds (e.g., secrecy error and correctness error) and may have limitations in applicability to real-world quantum systems with higher errors or different constraints. The security loss in dimension d for weak secrecy might be significant for large systems.