2007/04/30 by Jan Bouda, Mario Ziman
Computer Science · Engineering · Physics and Astronomy · #Entropy (arrow of time) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum capacity #Quantum channel #Quantum information #Quantum relative entropy #Qubit #Von Neumann entropy #Wireless Communication Security Techniques #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/20/011
published as J. Phys. A: Math. Theor. 40 (2007) 5415-5426 · no comment
openalex publication_date 2007/04/30 · arxiv created 2007/10/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel \cal E and von Neumann entropy of the ciphertext state \varrho(0). Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if exists) is optimizing the entropy. For non-ancillary single qubit PQC we have derived the optimal entropy for arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analyzed all the possible single qubit private quantum channels for arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.