Quantum Detection and Coding with Applications to Quantum Cryptography

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Analytical lower and upper bounds for the average error probability in M-ary quantum detection are derived. The upper bound is valid when the state ensemble, which can consist of pure or mixed states, satisfies a certain linear independence condition. The lower bound is generally valid and also has a classical interpretation. The quantum direct encryption protocol called AlphaEta is described, focusing on its equivalence under individual identical measurements by the eavesdropper to a classical random cipher. A new characterization of classical random ciphers is given that focuses on their potential security against known-plaintext attacks. The concept of a quantum random cipher is defined. The quantum random cipher characteristics of AlphaEta against phase and heterodyne measurements are elucidated. The derived lower and upper bounds on error probability are applied to the problem of security of AlphaEta under known-plaintext and ciphertext-only joint attacks. The system is shown to be insecure against known-plaintext attacks for sufficiently large known-plaintext regardless of the values of all system parameters. The eavesdropper's error probability is upper and lower bounded by expressions involving respectively the minimum and the maximum distance of the code generated by the underlying linear feedback shift register. For ciphertext-only attack, it is seen that the upper bound is not applicable to AlphaEta, leaving open the questions of security of AlphaEta and also the related key generation protocol AlphaEta-KG

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  • 05/07/2018
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