Zeng Xiang-Hua

Extended space for quantum cryptography using mixed states

A formulation is presented for quantum cryptography based on two mixed states in rigged Hilbert space. This is distinct from the usual scheme for quantum cryptography based on Hilbert space and Von Neumann quantum mechanics, excluding the effects of decoherence. We show that under specific conditions, the rigged Hilbert space formulation for quantum cryptography reduces to the Hilbert space formulation. However, there are opportunities for an eavesdropper on a secure channel to avoid detection using extended space techniques in the generalized functional space. In the generalized functional space, non-unitary operators can be constructed, that act on non-orthogonal mixed states without isometry; in this case, the no-cloning theorem for two non-orthogonal states is less efficient. Thus, functional space may provide a means for successfully implementing quantum cryptography.

Nonlinear conductivity for mesoscopic systems

A generalized Kubo formula for a mesoscopic system is derived describing the conductivity, subject to an (not weak) external electric field, and shown to be expressible in the Landauer–Buttiker form. Using this approach the electrical conductivity of a quantum dot point-contact was expressed as k(2e2/h), where k represents the strength of the mutual interactions. The conditions k 1, correspond to “repulsive” and “attractive” interactions with an external electric field, respectively, consistent with recent experimental data.