Различимость квантовых состояний и трудоемкость по Шеннону в квантовой криптографии
The proof of the security of quantum key distribution is a rather complex problem. Security is
defined in terms different from the requirements imposed on keys in classical cryptography. In quantum
cryptography, the security of keys is expressed in terms of the closeness of the quantum state of an eavesdropper
after key distribution to an ideal quantum state that is uncorrelated to the key of legitimate users. A metric
of closeness between two quantum states is given by the trace metric. In classical cryptography, the security
of keys is understood in terms of, say, the complexity of key search in the presence of side information.
In quantum cryptography, side information for the eavesdropper is given by the whole volume of information
on keys obtained from both quantum and classical channels. The fact that the mathematical apparatuses used
in the proof of key security in classical and quantum cryptography are essentially different leads to misunderstanding
and emotional discussions . Therefore, one should be able to answer the question of how different
cryptographic robustness criteria are related to each other. In the present study, it is shown that there is a
direct relationship between the security criterion in quantum cryptography, which is based on the trace distance
determining the distinguishability of quantum states, and the criterion in classical cryptography, which
uses guesswork on the determination of a key in the presence of side information.