Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem

Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show that the SIC existence problem is equivalent to three other, on the face of it quite different problems. Although it is still not clear whether these reformulations of the problem will make it more tractable, we believe that the fact that SICs have these connections to other areas of mathematics is of some intrinsic interest. Specifically, we reformulate the SIC problem in terms of (1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result being a greatly strengthened version of one previously obtained by Appleby, Flammia and Fuchs). The connection between these three reformulations is non-trivial: It is not easy to demonstrate their equivalence directly, without appealing to their common equivalence to SIC existence. In the course of our analysis we obtain a number of other results which may be of some independent interest.Comment: 36 pages, to appear in Quantum Inf. Compu

Criteria for Continuous-Variable Quantum Teleportation

We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of $0.58 \pm 0.02$ was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.Comment: 12 pages, to appear in Journal of Modern Optic

Dilepton production at HADES: theoretical predictions

Dileptons represent a unique probe for nuclear matter under extreme conditions reached in heavy-ion collisions. They allow to study meson properties, like mass and decay width, at various density and temperature regimes. Present days models allow generally a good description of dilepton spectra in ultra-relativistic heavy ion collision. For the energy regime of a few GeV/nucleon, important discrepancies between theory and experiment, known as the DLS puzzle, have been observed. Various models, including the one developed by the T\"{u}bingen group, have tried to address this problem, but have proven only partially successful. High precision spectra of dilepton emission in heavy-ion reactions at 1 and 2 GeV/nucleon will be released in the near future by the HADES Collaboration at GSI. Here we present the predictions for dilepton spectra in C+C reactions at 1 and 2 GeV/nucleon and investigate up to what degree possible scenarios for the in-medium modification of vector mesons properties are accessible by the HADES experiment.Comment: 12 pages, 4 figures; submitted to Phys.Lett.

Spin Coherence During Optical Excitation of a Single NV Center in Diamond

We examine the quantum spin state of a single nitrogen-vacancy (NV) center in diamond at room temperature as it makes a transition from the orbital ground-state (GS) to the orbital excited-state (ES) during non-resonant optical excitation. While the fluorescence read-out of NV-center spins relies on conservation of the longitudinal spin projection during optical excitation, the question of quantum phase preservation has not been examined. Using Ramsey measurements and quantum process tomography, we establish limits on NV center spin decoherence induced during optical excitation. Treating the optical excitation and ES spin precession as a quantum process, we measure a process fidelity of F=0.87\pm0.03, which includes ES spin dephasing during measurement. Extrapolation to the moment of optical excitation yields F\approx0.95. This result demonstrates that ES spin interactions may be used as a resource for quantum control because the quantum spin state can survive incoherent orbital transitions.Comment: 12 pages, 3 figure

Vector magnetic field microscopy using nitrogen vacancy centers in diamond

The localized spin triplet ground state of a nitrogen vacancy (NV) center in diamond can be used in atomic-scale detection of local magnetic fields. Here we present a technique using these defects in diamond to image fields around magnetic structures. We extract the local magnetic field vector by probing resonant transitions of the four fixed tetrahedral NV orientations. In combination with confocal microscopy techniques, we construct a 2-dimensional image of the local magnetic field vectors. Measurements are done in external fields less than 50 G and under ambient conditions.Comment: 9 pages, 3 figure

Spin Control of Drifting Electrons using Local Nuclear Polarization in Ferromagnet/Semiconductor Heterostructures

We demonstrate methods to locally control the spin rotation of moving electrons in a GaAs channel. The Larmor frequency of optically-injected spins is modulated when the spins are dragged through a region of spin-polarized nuclei created at a MnAs/GaAs interface. The effective field created by the nuclei is controlled either optically or electrically using the ferromagnetic proximity polarization effect. Spin rotation is also tuned by controlling the carrier traverse time through the polarized region. We demonstrate coherent spin rotations exceeding 4 pi radians during transport.Comment: 15 pages, 4 figure