Quantum Encryption and Generalized Quantum Shannon Impossibility
This work addresses foundational issues in quantum cryptography for researchers, providing incremental theoretical extensions to classical results.
The paper tackles the problem of extending Shannon's impossibility result to quantum encryption with imperfect secrecy and correctness, showing that a weaker secrecy definition implies a stronger one with a security loss dependent on the dimension of the quantum system, which is sufficient for target secrecy errors of o(d^{-1}).
The famous Shannon impossibility result says that any encryption scheme with perfect secrecy requires a secret key at least as long as the message. In this paper we provide its quantum analogue with imperfect secrecy and imperfect correctness. We also give a systematic study of information-theoretically secure quantum encryption with two secrecy definitions. We show that the weaker one implies the stronger but with a security loss in $d$, where $d$ is the dimension of the encrypted quantum system. This is good enough if the target secrecy error is of $o(d^{-1})$.