Remote Preparation of Mixed States via Noisy Entanglement

We present a practical and general scheme of remote preparation for pure and mixed state, in which an auxiliary qubit and controlled-NOT gate are used. We discuss the remote state preparation (RSP) in two important types of decoherent channel (depolarizing and dephaseing). In our experiment, we realize RSP in the dephaseing channel by using spontaneous parametric down conversion (SPDC), linear optical elements and single photon detector.Comment: 10 pages, 5 figures, submitted to PR

Conservation law of harmonic mappings in supercritical dimensions

In this short note, we provide a partial extension of Rivi\`ere's convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.Comment: 6 page