Factorization of nonnegative matrices—II

AbstractSuppose A is an n×n nonnegative matrix. Necessary and sufficient conditions are given for A to be factored as LU, where L is a lower triangular nonnegative matrix, and U is an upper triangular nonnegative matrix with uii = 1

Properties of implanted and CVD incorporated nitrogen-vacancy centers: preferential charge state and preferential orientation

The combination of the long electron state spin coherence time and the optical coupling of the ground electronic states to an excited state manifold makes the nitrogen-vacancy (NV) center in diamond an attractive candidate for quantum information processing. To date the best spin and optical properties have been found in centers deep within the diamond crystal. For useful devices it will be necessary to engineer NVs with similar properties close to the diamond surface. We report on properties including charge state control and preferential orientation for near surface NVs formed either in CVD growth or through implantation and annealing

Remarks on Duality Transformations and Generalized Stabilizer States

We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well as exact characterizations of ground states employing non-Hermitean eigenvalue equations and use this to motivate a generalization of the stabilizer formalism to non-Hermitean operators. The resulting class of states is larger than that of standard stabilizer states and allows for example for continuous variation of local entropies rather than the discrete values taken on stabilizer states and the exact description of certain ground states of Hamilton operators.Comment: Contribution to Special Issue in Journal of Modern Optics celebrating the 60th birthday of Peter Knigh

Quantum interference of single photons from remote nitrogen-vacancy centers in diamond

We demonstrate quantum interference between indistinguishable photons emitted by two nitrogen-vacancy (NV) centers in distinct diamond samples separated by two meters. Macroscopic solid immersion lenses are used to enhance photon collection efficiency. Quantum interference is verified by measuring a value of the second-order cross-correlation function $g^{(2)}(0) = 0.35 \pm 0.04<0.5$. In addition, optical transition frequencies of two separated NV centers are tuned into resonance with each other by applying external electric fields. Extension of the present approach to generate entanglement of remote solid-state qubits is discussed.Comment: 5 pages, 3 figure

Direct evaluation of pure graph state entanglement

We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory, namely the identification of maximum independent set, allows us to evaluate three multipartite entanglement measures for pure graph states. We construct the minimal linear decomposition into product states for a large group of pure graph states, allowing us to evaluate the Schmidt measure. Furthermore we show that computation of distance-like measures such as relative entropy of entanglement and geometric measure becomes tractable for these states by explicit construction of closest separable and closest product states respectively. We show how these separable states can be described using stabiliser formalism as well as PEPs-like construction. Finally we discuss the way in which introducing noise to the system can optimally destroy entanglement.Comment: 23 pages, 9 figure

The Perspective of College Seniors in ROTC on Becoming a Commissioned Officer

While there is growing research into Military and Mental health issues, the focus of such research has primarily been restricted to those populations who are retired from Military or who step-down from Active Duty. Following a case study with Reservists, we became aware that mental health issues in the Military Population may potentially stem from concepts involved the initial training phases. With the hypothesis that ROTC Cadets are among the youngest persons engaging in Military training, we approached ROTC Air Force and ROTC Army Cadets who were Seniors by credit at Cedarville University. The Cadets were asked to participate in a face-to-face interview with a researcher, to share their experiences of ROTC and their perspectives on what life as a Commissioned Officer would be like. Participation in the interviews was voluntary, but the Air Force Commander and Army Commander had informed their Cadets that this study had been approved by them and participation was encouraged. Participants included both male and female Cadets from a broad range of academic majors. The interviews were analyzed and six themes emerged:- (a) Being associated with high caliber professionals (b) Balancing military persona with non-military persona (c) Skills and strategies for success in life (d) Personal values (e) Awareness of challenges (f) Impact of training on persona. Overall, the Cadets expressed excitement at the prospect of becoming Commissioned Officers, and pride in being among those who serve their country

Full stress tensor measurement using colour centres in diamond

Stress and strain are important factors in determining the mechanical, electronic, and optical properties of materials, relating to each other by the material's elasticity or stiffness. Both are represented by second rank field tensors with, in general, six independent components. Measurements of these quantities are usually achieved by measuring a property that depends on the translational symmetry and periodicity of the crystal lattice, such as optical phonon energies using Raman spectroscopy, the electronic band gap using cathodoluminescence, photoelasticity via the optical birefringence, or Electron Back Scattering Diffraction (EBSD). A reciprocal relationship therefore exists between the maximum sensitivity of the measurements and the spatial resolution. Furthermore, of these techniques, only EBSD and off-axis Raman spectroscopy allow measurement of all six components of the stress tensor, but neither is able to provide full 3D maps. Here we demonstrate a method for measuring the full stress tensor in diamond, using the spectral and optical polarization properties of the photoluminescence from individual nitrogen vacancy (NV) colour centres. We demonstrate a sensitivity of order 10 MPa, limited by local fluctuations in the stress in the sample, and corresponding to a strain of about 10^-5, comparable with the best sensitivity provided by other techniques. By using the colour centres as built-in local sensors, the technique overcomes the reciprocal relationship between spatial resolution and sensitivity and offers the potential for measuring strains as small as 10^-9 at spatial resolution of order 10 nm. Furthermore it provides a straightforward route to volumetric stress mapping. Aside from its value in understanding strain distributions in diamond, this new approach to stress and strain measurement could be adapted for use in micro or nanoscale sensors.Comment: 12 pages, 5 figures - supplementary informations included in appendi