Connections and Metrics Respecting Standard Purification

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.Comment: Latex, 27 page

On the Apparent Orbital Inclination Change of the Extrasolar Transiting Planet TrES-2b

On June 15, 2009 UT the transit of TrES-2b was detected using the University of Arizona's 1.55 meter Kuiper Telescope with 2.0-2.5 millimag RMS accuracy in the I-band. We find a central transit time of $T_c = 2454997.76286 \pm0.00035$ HJD, an orbital period of $P = 2.4706127 \pm 0.0000009$ days, and an inclination angle of $i = 83^{\circ}.92 \pm 0.05$, which is consistent with our re-fit of the original I-band light curve of O'Donovan et al. (2006) where we find $i = 83^{\circ}.84 \pm0.05$. We calculate an insignificant inclination change of $\Delta i = -0^{\circ}.08 \pm 0.07$ over the last 3 years, and as such, our observations rule out, at the $\sim 11 \sigma$ level, the apparent change of orbital inclination to $i_{predicted} = 83^{\circ}.35 \pm0.1$ as predicted by Mislis and Schmitt (2009) and Mislis et al. (2010) for our epoch. Moreover, our analysis of a recently published Kepler Space Telescope light curve (Gilliland et al. 2010) for TrES-2b finds an inclination of $i = 83^{\circ}.91 \pm0.03$ for a similar epoch. These Kepler results definitively rule out change in $i$ as a function of time. Indeed, we detect no significant changes in any of the orbital parameters of TrES-2b.Comment: 19 pages, 1 table, 7 figures. Re-submitted to ApJ, January 14, 201

Bures volume of the set of mixed quantum states

We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the boundary of the set M_N and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N.Comment: 15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) correcte

Two-Qubit Separability Probabilities and Beta Functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and reorganized, with the quasi-Monte Carlo integration sample size being greatly increase

Follow-up Observations of the Neptune Mass Transiting Extrasolar Planet HAT-P-11b

We have confirmed the existence of the transiting super Neptune extrasolar planet HAT-P-11b. On May 1, 2009 UT the transit of HAT-P-11b was detected at the University of Arizona's 1.55m Kuiper Telescope with 1.7 millimag rms accuracy. We find a central transit time of T_c = 2454952.92534+/-0.00060 BJD; this transit occurred 80+/-73 seconds sooner than previous measurements (71 orbits in the past) would have predicted. Hence, our transit timing rules out the presence of any large (>200 s) deviations from the ephemeris of Bakos et al. (2009). We obtain a slightly more accurate period of P=4.8878045+/-0.0000043 days. We measure a slightly larger planetary radius of R_p=0.452+/-0.020 R_J (5.07+/-0.22 R_earth) compared to Bakos and co-workers' value of 0.422+/-0.014 R_J (4.73+/-0.16 R_earth). Our values confirm that HAT-P-11b is very similar to GJ 436b (the only other known transiting super Neptune) in radius and other bulk properties.Comment: accepted to ApJ Letters, 11 pages, 2 figures (see Dittmann et al. 2009 ApJ 699 L48-L51

Commonwealth Marine Reserves Review: Report of the Expert Scientific Panel

The report provides a scientific basis for the declaration and management of the Australian Marine Reserve Syste

A team approach to the indication for gender reassignment surgery in transsexuals resulting in long-term outcome improvement

At the University of Basel (Switzerland), a multidisciplinary team was established for pre-operative selection and treatment of patients with gender dysphoria. As a result, the indications for surgical gender reassignment could be judged with considerably greater accuracy than previously possible. In the 9-year period of this prospective study only 14 of 57 patients with gender dysphoria were selected for surgical treatment. At the time of this survey, six patients are still under psychiatric preoperative evaluation, and six further male-to-female transsexuals are under hormonal treatment awaiting surgery. Following the operation, only one of nine male-to-female patients is socially unstable and that patient's quality of life is worse than prior to gender reassignment. Of the female-to-male transsexuals, all four are stable in their professional and family relations. In conclusion, a comprehensive evaluation of patients with gender dysphoria and the conclusive indications established within the team considerably improved the postoperative outcome of gender reassignmen