A Simple Quantum Statistical Interpretation of the Key Secrecy Criterion in Quantum Cryptography

Abstract

In spite of the fact that quantum cryptography is currently the only field of quantum informatics that has been developed from the fundamental physical principles of quantum mechanics to practical applications in the field of transmission and security of information, many results remain, in our opinion, obscure to a wide physics community. The goal of the present study is to give, using minimal and simple mathematical tools, a simple and physically intuitively clear interpretation of the central result of quantum cryptography—a key secrecy criterion based on the trace metric—the distance between two quantum states. The interpretation proposed is self-sufficient and uses the standard Born quantum statistical interpretation of the density matrix—a quantum ensemble—a statistical mixture of quantum states.