Symmetric mixed states of nn qubits: local unitary stabilizers and entanglement classes

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for published versio

Linear to Circular Polarisation Conversion using Birefringent Properties of Aligned Crystals for Multi-GeV Photons

We present the first experimental results on the use of a thick aligned Si crystal acting as a quarter wave plate to induce a degree of circular polarisation in a high energy linearly polarised photon beam. The linearly polarised photon beam is produced from coherent bremsstrahlung radiation by 178 GeV unpolarised electrons incident on an aligned Si crystal, acting as a radiator. The linear polarisation of the photon beam is characterised by measuring the asymmetry in electron-positron pair production in a Ge crystal, for different crystal orientations. The Ge crystal therefore acts as an analyser. The birefringence phenomenon, which converts the linear polarisation to circular polarisation, is observed by letting the linearly polarised photons beam pass through a thick Si quarter wave plate crystal, and then measuring the asymmetry in electron-positron pair production again for a selection of relative angles between the crystallographic planes of the radiator, analyser and quarter wave plate. The systematics of the difference between the measured asymmetries with and without the quarter wave plate are predicted by theory to reveal an evolution in the Stokes parameters from which the appearance of a circularly polarised component in the photon beam can be demonstrated. The measured magnitude of the circularly polarised component was consistent with the theoretical predictions, and therefore is in indication of the existence of the birefringence effect.Comment: 12 pages, 12 figures, 1 table, REVTeX4 two column, Version for publicatio

Coherent bremsstrahlung, boherent pair production, birefringence and polarimetry in the 20-170 GeV energy range using aligned crystals

The processes of coherent bremsstrahlung (CB) and coherent pair production (CPP) based on aligned crystal targets have been studied in the energy range 20-170 GeV. The experimental arrangement allowed for measurements of single photon properties of these phenomena including their polarization dependences. This is significant as the theoretical description of CB and CPP is an area of active theoretical debate and development. With the theoretical approach used in this paper both the measured cross sections and polarization observables are predicted very well. This indicates a proper understanding of CB and CPP up to energies of 170 GeV. Birefringence in CPP on aligned crystals is applied to determine the polarization parameters in our measurements. New technologies for high energy photon beam optics including phase plates and polarimeters for linear and circular polarization are demonstrated in this experiment. Coherent bremsstrahlung for the strings-on-strings (SOS) orientation yields a larger enhancement for hard photons than CB for the channeling orientations of the crystal. Our measurements and our calculations indicate low photon polarizations for the high energy SOS photons.Comment: 23 pages, 27 figures, 2 tables, REVTeX4 two column

Coherent Pair Production by Photons in the 20-170 GeV Energy Range Incident on Crystals and Birefringence

The cross section for coherent pair production by linearly polarised photons in the 20-170 GeV energy range was measured for photon aligned incidence on ultra-high quality diamond and germanium crystals. The theoretical description of coherent bremsstrahlung and coherent pair production phenomena is an area of active theoretical debate and development. However, under our experimental conditions, the theory predicted the combined cross section and polarisation experimental observables very well indeed. In macroscopic terms, our experiment measured a birefringence effect in pair production in a crystal. This study of this effect also constituted a measurement of the energy dependent linear polarisation of photons produced by coherent bremsstrahlung in aligned crystals. New technologies for manipulating high energy photon beams can be realised based on an improved understanding of QED phenomena at these energies. In particular, this experiment demonstrates an efficient new polarimetry technique. The pair production measurements were done using two independent methods simultaneously. The more complex method using a magnet spectrometer showed that the simpler method using a multiplicity detector was also viable.Comment: 10 pages, 13 figures, 1 table, REVTeX4 two column, Version for publicatio

Results on the Coherent Interaction of High Energy Electrons and Photons in Oriented Single Crystals

The CERN-NA-59 experiment examined a wide range of electromagnetic processes for multi-GeV electrons and photons interacting with oriented single crystals. The various types of crystals and their orientations were used for producing photon beams and for converting and measuring their polarisation. The radiation emitted by 178 GeV unpolarised electrons incident on a 1.5 cm thick Si crystal oriented in the Coherent Bremsstrahlung (CB) and the String-of-Strings (SOS) modes was used to obtain multi-GeV linearly polarised photon beams. A new crystal polarimetry technique was established for measuring the linear polarisation of the photon beam. The polarimeter is based on the dependence of the Coherent Pair Production (CPP) cross section in oriented single crystals on the direction of the photon polarisation with respect to the crystal plane. Both a 1 mm thick single crystal of Germanium and a 4 mm thick multi-tile set of synthetic Diamond crystals were used as analyzers of the linear polarisation. A birefringence phenomenon, the conversion of the linear polarisation of the photon beam into circular polarisation, was observed. This was achieved by letting the linearly polarised photon beam pass through a 10 cm thick Silicon single crystal that acted as a "quarter wave plate" (QWP) as suggested by N. Cabibbo et al.Comment: Presented at International workshop "Relativistic Channeling and Related Coherent Phenomena", Frascati (Rome) 23-26 March 200

Measurement of CP Asymmetries and Branching Fractions in Charmless Two-Body B-Meson Decays to Pions and Kaons

We present improved measurements of CP-violation parameters in the decays $B^0 \to \pi^+ \pi^-$, $B^0 \to K^+ \pi^-$, and $B^0 \to \pi^0 \pi^0$, and of the branching fractions for $B^0 \to \pi^0 \pi^0$ and $B^0 \to K^0 \pi^0$. The results are obtained with the full data set collected at the $\Upsilon(4S)$ resonance by the BABAR experiment at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory, corresponding to $467 \pm 5$ million $B\bar B$ pairs. We find the CP-violation parameter values and branching fractions $S_{\pi^+\pi^-} = -0.68 \pm 0.10 \pm 0.03, C_{\pi^+\pi^-} = -0.25 \pm 0.08 \pm 0.02, A_{K^-\pi^+} = -0.107 \pm 0.016 ^{+0.006}_{-0.004}, C_{\pi^0\pi^0} = -0.43 \pm 0.26 \pm 0.05, Br(B^0 \to \pi^0 \pi^0) = (1.83 \pm 0.21 \pm 0.13) \times 10^{-6}, Br(B^0 \to K^0 \pi^0) = (10.1 \pm 0.6 \pm 0.4) \times 10^{-6},$ where in each case, the first uncertainties are statistical and the second are systematic. We observe CP violation with a significance of 6.7 standard deviations for $B^0 \to\pi^+\pi^-$ and 6.1 standard deviations for $B^0 \to K^+ \pi^-$, including systematic uncertainties. Constraints on the Unitarity Triangle angle $\alpha$ are determined from the isospin relations among the $B \to \pi\pi$ rates and asymmetries. Considering only the solution preferred by the Standard Model, we find $\alpha$ to be in the range $[71^\circ,109^\circ]$ at the 68% confidence level.Comment: 18 pages, 11 postscript figures, submitted to Phys. Rev.

Measurement of the Time-Dependent CP Asymmetry of Partially Reconstructed B0->D*+D*- Decays

We present a new measurement of the time-dependent CP asymmetry of B0->D*+D*- decays using (471+-5) million BBbar pairs collected with the BaBar detector at the PEP-II B Factory at the SLAC National Accelerator Laboratory. Using the technique of partial reconstruction, we measure the time-dependent CP asymmetry parameters S=-0.34+-0.12+-0.05$ and C=+0.15+-0.09+-0.04. Using the value for the CP-odd fraction R_perp=0.158+-0.028+-0.006, previously measured by BaBar with fully reconstructed B0->D*+D*- events, we extract the CP-even components S+=-0.49+-0.18+-0.07+-0.04 and C+=+0.15+-0.09+-0.04. In each case, the first uncertainty is statistical and the second is systematic; the third uncertainty on S+ is the contribution from the uncertainty on R_perp. The measured value of the CP-even component S+ is consistent with the value of sin(2Beta) measured in b->(ccbar)s transitions, and with the Standard Model expectation of small penguin contributions.Comment: 17 pages, 7 figures, submitted to Physical Review

Search for lepton-number violating processes in B+ -> h- l+ l+ decays

We have searched for the lepton-number violating processes B+ -> h- l+ l+ with h- = K-/pi- and l+ = e+/mu+, using a sample of 471+/-3 million BBbar events collected with the BaBar detector at the PEP-II e+e- collider at the SLAC National Accelerator Laboratory. We find no evidence for these decays and place 90% confidence level upper limits on their branching fractions Br(B+ -> pi- e+ e+) K- e+ e+) pi- mu+ mu+) K- mu+ mu+) < 6.7 x 10^{-8}.Comment: 8 pages, 4 postscript figures, submitted to Phys. Rev. D. R

Measurement of B(B-->X_s {\gamma}), the B-->X_s {\gamma} photon energy spectrum, and the direct CP asymmetry in B-->X_{s+d} {\gamma} decays

The photon spectrum in B --> X_s {\gamma} decay, where X_s is any strange hadronic state, is studied using a data sample of (382.8\pm 4.2) \times 10^6 e^+ e^- --> \Upsilon(4S) --> BBbar events collected by the BABAR experiment at the PEP-II collider. The spectrum is used to measure the branching fraction B(B --> X_s \gamma) = (3.21 \pm 0.15 \pm 0.29 \pm 0.08)\times 10^{-4} and the first, second, and third moments = 2.267 \pm 0.019 \pm 0.032 \pm 0.003 GeV,, )^2> = 0.0484 \pm 0.0053 \pm 0.0077 \pm 0.0005 GeV^2, and )^3> = -0.0048 \pm 0.0011 \pm 0.0011 \pm 0.0004 GeV^3, for the range E_\gamma > 1.8 GeV, where E_{\gamma} is the photon energy in the B-meson rest frame. Results are also presented for narrower E_{\gamma} ranges. In addition, the direct CP asymmetry A_{CP}(B --> X_{s+d} \gamma) is measured to be 0.057 \pm 0.063. The spectrum itself is also unfolded to the B-meson rest frame; that is the frame in which theoretical predictions for its shape are made.Comment: 37 pages, 19 postscript figures, submitted to Phys. Rev. D. No analysis or results have changed from previous version. Some changes to improve clarity based on interactions with Phys. Rev. D referees, including one new Figure (Fig. 13), and some minor wording/punctuation/spelling mistakes fixe