Selection from read-only memory with limited workspace

Given an unordered array of $N$ elements drawn from a totally ordered set and an integer $k$ in the range from $1$ to $N$, in the classic selection problem the task is to find the $k$-th smallest element in the array. We study the complexity of this problem in the space-restricted random-access model: The input array is stored on read-only memory, and the algorithm has access to a limited amount of workspace. We prove that the linear-time prune-and-search algorithm---presented in most textbooks on algorithms---can be modified to use $\Theta(N)$ bits instead of $\Theta(N)$ words of extra space. Prior to our work, the best known algorithm by Frederickson could perform the task with $\Theta(N)$ bits of extra space in $O(N \lg^{*} N)$ time. Our result separates the space-restricted random-access model and the multi-pass streaming model, since we can surpass the $\Omega(N \lg^{*} N)$ lower bound known for the latter model. We also generalize our algorithm for the case when the size of the workspace is $\Theta(S)$ bits, where $\lg^3{N} \leq S \leq N$. The running time of our generalized algorithm is $O(N \lg^{*}(N/S) + N (\lg N) / \lg{} S)$, slightly improving over the $O(N \lg^{*}(N (\lg N)/S) + N (\lg N) / \lg{} S)$ bound of Frederickson's algorithm. To obtain the improvements mentioned above, we developed a new data structure, called the wavelet stack, that we use for repeated pruning. We expect the wavelet stack to be a useful tool in other applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201

A high bandwidth quantum repeater

We present a physical- and link-level design for the creation of entangled pairs to be used in quantum repeater applications where one can control the noise level of the initially distributed pairs. The system can tune dynamically, trading initial fidelity for success probability, from high fidelity pairs (F=0.98 or above) to moderate fidelity pairs. The same physical resources that create the long-distance entanglement are used to implement the local gates required for entanglement purification and swapping, creating a homogeneous repeater architecture. Optimizing the noise properties of the initially distributed pairs significantly improves the rate of generating long-distance Bell pairs. Finally, we discuss the performance trade-off between spatial and temporal resources.Comment: 5 page

Efficient optical quantum information processing

Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular appeal, since it offers the prospect of communicating and computing with the same type of qubit. Linear optical techniques have been shown to be scalable, but the corresponding quantum computing circuits need many auxiliary resources. Here we present an alternative approach to optical QIP, based on the use of weak cross-Kerr nonlinearities and homodyne measurements. We show how this approach provides the fundamental building blocks for highly efficient non-absorbing single photon number resolving detectors, two qubit parity detectors, Bell state measurements and finally near deterministic control-not (CNOT) gates. These are essential QIP devicesComment: Accepted to the Journal of optics B special issue on optical quantum computation; References update

Weak non-linearities and cluster states

We propose a scalable approach to building cluster states of matter qubits using coherent states of light. Recent work on the subject relies on the use of single photonic qubits in the measurement process. These schemes have a low initial success probability and low detector efficiencies cause a serious blowup in resources. In contrast, our approach uses continuous variables and highly efficient measurements. We present a two-qubit scheme, with a simple homodyne measurement system yielding an entangling operation with success probability 1/2. Then we extend this to a three-qubit interaction, increasing this probability to 3/4. We discuss the important issues of the overhead cost and the time scaling, showing how these can be vastly improved with access to this new probability range.Comment: 5 pages, to appear in Phys. Rev.

Applications of Coherent Population Transfer to Quantum Information Processing

We develop a theoretical framework for the exploration of quantum mechanical coherent population transfer phenomena, with the ultimate goal of constructing faithful models of devices for classical and quantum information processing applications. We begin by outlining a general formalism for weak-field quantum optics in the Schr\"{o}dinger picture, and we include a general phenomenological representation of Lindblad decoherence mechanisms. We use this formalism to describe the interaction of a single stationary multilevel atom with one or more propagating classical or quantum laser fields, and we describe in detail several manifestations and applications of electromagnetically induced transparency. In addition to providing a clear description of the nonlinear optical characteristics of electromagnetically transparent systems that lead to ``ultraslow light,'' we verify that -- in principle -- a multi-particle atomic or molecular system could be used as either a low power optical switch or a quantum phase shifter. However, we demonstrate that the presence of significant dephasing effects destroys the induced transparency, and that increasing the number of particles weakly interacting with the probe field only reduces the nonlinearity further. Finally, a detailed calculation of the relative quantum phase induced by a system of atoms on a superposition of spatially distinct Fock states predicts that a significant quasi-Kerr nonlinearity and a low entropy cannot be simultaneously achieved in the presence of arbitrary spontaneous emission rates. Within our model, we identify the constraints that need to be met for this system to act as a one-qubit and a two-qubit conditional phase gate.Comment: 25 pages, 14 figure

Leading the evaluation of institutional online learning environments for quality enhancement in times of change

This paper reports on findings from a nationally funded project which aims to design and implement a quality management framework for online learning environments (OLEs). Evaluation is a key component of any quality management system and it is this aspect of the framework that is the focus of this paper. In developing the framework initial focus groups were conducted at the five participating institutions. These revealed that, although regarded as important, there did not appear to be a shared understanding of the nature and purpose of evaluation. A second series of focus groups revealed there were multiple perspectives arising from those with a vested interest in online learning. These perspectives will be outlined. Overall, how evaluation was undertaken was highly variable within and across the five institutions reflecting where they were at in relation to the development of their OLE

Sediment resuspension and erosion by vortex rings

Particle resuspension and erosion induced by a vortex ringinteracting with a sediment layer was investigated experimentally using flow visualization (particle image velocimetry), high-speed video, and a recently developed light attenuation method for measuring displacements in bed level. Near-spherical sediment particles were used throughout with relative densities of 1.2–7 and diameters (d)(d) ranging between 90 and 1600 μm1600 μm. Attention was focused on initially smooth, horizontal bedforms with the vortex ring aligned to approach the bed vertically. Interaction characteristics were investigated in terms of the dimensionless Shields parameter, defined using the vortex-ring propagation speed. The critical conditions for resuspension (whereby particles are only just resuspended) were determined as a function of particle Reynolds number (based on the particle settling velocity and dd). The effects of viscous damping were found to be significant for d/δ<15d/δ<15, where δδ denotes the viscous sublayer thickness. Measurements of bed deformation were obtained during the interaction period, for a range of impact conditions. The (azimuthal) mean crater profile is shown to be generally self-similar during the interaction period, except for the most energetic impacts and larger sediment types. Loss of similarity occurs when the local bed slope approaches the repose limit, leading to collapse. Erosion, deposition, and resuspension volumes are analyzed as a function interaction time, impact condition, and sediment size

Contiguous polarisation spectra of the Earth from 300 to 850 nm measured by GOME-2 onboard MetOp-A

In this paper we present the first contiguous high-resolution spectra of the Earth's polarisation observed by a satellite instrument. The measurements of the Stokes fraction <i>Q/I</i> are performed by the spectrometer GOME-2 onboard the MetOp-A satellite. Polarisation measurements by GOME-2 are performed by onboard polarisation measurement devices (PMDs) and the high-resolution measurements discussed in this paper are taken in the special "PMD RAW" mode of operation. The spectral resolution of these PMD RAW polarisation measurements varies from 3 nm in the ultraviolet (UV) to 35 nm in the near-infrared wavelength range. We first compare measurements of the polarisation from cloud-free scenes with radiative transfer calculations for a number of cases. We find good agreement but also a spectral discrepancy at 800 nm, which we attribute to remaining imperfections in the calibration key data. Secondly, we study the polarisation of scenes with special scattering geometries that normally lead to near-zero <i>Q/I</i>. The GOME-2 polarisation spectra indeed show this behaviour and confirm the existence of the small discrepancy found earlier. Thirdly, we study the Earth polarisation for a variety of scenes. This provides a blueprint of <i>Q/I</i> over land and sea surfaces for various degrees of cloud cover. Fourthly, we compare the spectral dependence of measurements of <i>Q/I</i> in the UV with the generalised distribution function proposed by Schutgens and Stammes (2002) to describe the shape of the UV polarisation spectrum. The GOME-2 data confirm that these functions match the spectral behaviour captured by the GOME-2 PMD RAW mode

Secure self-calibrating quantum random bit generator

Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the "min-entropy" of the system, and we employ this value to distill a truly random bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.Comment: 5 pages, 2 figure