Abstract

Strong attacks against quantum key distribution use quantum memories and quantum gates to attack directly the final key. In this paper we extend a novel security result recently obtained, to demonstrate proofs of security against a wide class of such attacks. To reach this goal we calculate information-dependent reduced density matrices, we study the geometry of quantum mixed state, and we find bounds on the information leaked to an eavesdropper. Our result suggests that quantum cryptography is ultimately secure. Quantum cryptography (e.g. [1, 2]) suggests an information secure key distribution. It is based on the fact that non-orthogonal quantum states cannot be cloned, and any attempt to obtain information regarding these states necessarily disturbs them and induces noise. In principle, the legitimate users of a quantum key distribution scheme, Alice and Bob, should quit the protocol if they notice a noise. However, in real protocols, the channels and

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