Bounds on Information and the Security of Quantum Cryptography

In this paper we use properties of quantum mixed states to find bounds on various measures of their distinguishability. These bounds are used for analyzing strong joint attacks against quantum key distribution which use quantum probes, quantum memories, and quantum gates to attack directly the final key. We present a wide class of joint attacks, and we prove security against them. [S0031-9007(97)04463-3] PACS numbers: 89.70. + c, 02.50. ‐ r, 03.65.Bz, 89.80. + h Various types of measures of information which can be obtained from quantum states (which are also measures of distinguishability of the quantum states) are useful for the analysis of the security of quantum cryptography. In many cases upper bounds on the information suffice. Moreover, when the exact calculation is unknown, there are no alternatives. In this paper we present new types of bounds on such measures and we use these bounds to prove security against a large class of attacks on quantum key distribution. These bounds are very simple and general, and they can be found useful for other tasks in quantum information and computation.