The Dirichlet-to-Robin Transform

A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact construction of the Green functions for the wave, heat, and Schrodinger problems with a Robin boundary condition. The resulting physical picture is that the field can exchange energy with the boundary, and a delayed reflection from the boundary results. In more general situations the method allows at least approximate and local construction of the appropriate reflected solutions, and hence a "classical path" analysis of the Green functions and the associated spectral information. By this method we solve the wave equation on an interval with one Robin and one Dirichlet endpoint, and thence derive several variants of a Gutzwiller-type expansion for the density of eigenvalues. The variants are consistent except for an interesting subtlety of distributional convergence that affects only the neighborhood of zero in the frequency variable.Comment: 31 pages, 5 figures; RevTe

Positioning and clock synchronization through entanglement

A method is proposed to employ entangled and squeezed light for determining the position of a party and for synchronizing distant clocks. An accuracy gain over analogous protocols that employ classical resources is demonstrated and a quantum-cryptographic positioning application is given, which allows only trusted parties to learn the position of whatever must be localized. The presence of a lossy channel and imperfect photodetection is considered. The advantages in using partially entangled states is discussed.Comment: Revised version. 9 pages, 6 figure

Approaching the Heisenberg limit with two mode squeezed states

Two mode squeezed states can be used to achieve Heisenberg limit scaling in interferometry: a phase shift of $\delta \phi \approx 2.76 /$ can be resolved. The proposed scheme relies on balanced homodyne detection and can be implemented with current technology. The most important experimental imperfections are studied and their impact quantified.Comment: 4 pages, 7 figure

From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on "Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus Memorial Issue); v2: minor change

Patient/Family Education for Newly Diagnosed Pediatric Oncology Patients

There is a paucity of data to support evidence-based practices in the provision of patient/family education in the context of a new childhood cancer diagnosis. Since the majority of children with cancer are treated on pediatric oncology clinical trials, lack of effective patient/family education has the potential to negatively affect both patient and clinical trial outcomes. The Children’s Oncology Group Nursing Discipline convened an interprofessional expert panel from within and beyond pediatric oncology to review available and emerging evidence and develop expert consensus recommendations regarding harmonization of patient/family education practices for newly diagnosed pediatric oncology patients across institutions. Five broad principles, with associated recommendations, were identified by the panel, including recognition that (1) in pediatric oncology, patient/family education is family-centered; (2) a diagnosis of childhood cancer is overwhelming and the family needs time to process the diagnosis and develop a plan for managing ongoing life demands before they can successfully learn to care for the child; (3) patient/family education should be an interprofessional endeavor with 3 key areas of focus: (a) diagnosis/treatment, (b) psychosocial coping, and (c) care of the child; (4) patient/family education should occur across the continuum of care; and (5) a supportive environment is necessary to optimize learning. Dissemination and implementation of these recommendations will set the stage for future studies that aim to develop evidence to inform best practices, and ultimately to establish the standard of care for effective patient/family education in pediatric oncology

Entanglement and visibility at the output of a Mach-Zehnder interferometer

We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal phase-shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuum at the input leads to maximum entangled state at the output. The fringes visibilities resulting from measuring the coincidence counting rate or the squared difference photocurrent are evaluated and compared each other. Homodyne-like detection turns out to be preferable in almost all situations, with the exception of the very low signals regime.Comment: 6 figs, accepted for publication on PRA, see also http://enterprise.pv.infn.it/~pari

Purity of Gaussian states: measurement schemes and time-evolution in noisy channels

We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate quadratures is necessary and sufficient to determine the purity at any time. The statistical reliability and the range of applicability of the proposed measurement scheme is tested by means of Monte Carlo simulated experiments. We then consider the dynamics of purity in noisy channels. We derive an evolution equation for the purity of general Gaussian states both in thermal and squeezed thermal baths. We show that purity is maximized at any given time for an initial coherent state evolving in a thermal bath, or for an initial squeezed state evolving in a squeezed thermal bath whose asymptotic squeezing is orthogonal to that of the input state.Comment: 9 Pages, 6 Figures; minor errors correcte

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion

We perform a quantum theoretical calculation of the noise power spectrum for a phase measurement of the light output from a coherently driven optical cavity with a freely moving rear mirror. We examine how the noise resulting from the quantum back action appears among the various contributions from other noise sources. We do not assume an ideal (homodyne) phase measurement, but rather consider phase modulation detection, which we show has a different shot noise level. We also take into account the effects of thermal damping of the mirror, losses within the cavity, and classical laser noise. We relate our theoretical results to experimental parameters, so as to make direct comparisons with current experiments simple. We also show that in this situation, the standard Brownian motion master equation is inadequate for describing the thermal damping of the mirror, as it produces a spurious term in the steady-state phase fluctuation spectrum. The corrected Brownian motion master equation [L. Diosi, Europhys. Lett. {\bf 22}, 1 (1993)] rectifies this inadequacy.Comment: 12 pages revtex, 2 figure