Two-message quantum interactive proofs and the quantum separability problem

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum circuit produce a state that is separable or entangled? Here, we give evidence that it is computationally hard to decide the answer to this question, even if one has access to the power of quantum computation. We begin by exhibiting a two-message quantum interactive proof system that can decide the answer to a promise version of the question. We then prove that the promise problem is hard for the class of promise problems with "quantum statistical zero knowledge" (QSZK) proof systems by demonstrating a polynomial-time Karp reduction from the QSZK-complete promise problem "quantum state distinguishability" to our quantum separability problem. By exploiting Knill's efficient encoding of a matrix description of a state into a description of a circuit to generate the state, we can show that our promise problem is NP-hard with respect to Cook reductions. Thus, the quantum separability problem (as phrased above) constitutes the first nontrivial promise problem decidable by a two-message quantum interactive proof system while being hard for both NP and QSZK. We also consider a variant of the problem, in which a given polynomial-time mixed-state quantum circuit accepts a quantum state as input, and the question is to decide if there is an input to this circuit which makes its output separable across some bipartite cut. We prove that this problem is a complete promise problem for the class QIP of problems decidable by quantum interactive proof systems. Finally, we show that a two-message quantum interactive proof system can also decide a multipartite generalization of the quantum separability problem.Comment: 34 pages, 6 figures; v2: technical improvements and new result for the multipartite quantum separability problem; v3: minor changes to address referee comments, accepted for presentation at the 2013 IEEE Conference on Computational Complexity; v4: changed problem names; v5: updated references and added a paragraph to the conclusion to connect with prior work on separability testin

Quantum interactive proofs and the complexity of separability testing

We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), and QSZK), there corresponds a natural separability testing problem that is complete for that class. Of particular interest is the fact that the problem of determining whether an isometry can be made to produce a separable state is either QMA-complete or QMA(2)-complete, depending upon whether the distance between quantum states is measured by the one-way LOCC norm or the trace norm. We obtain strong hardness results by proving that for each n-qubit maximally entangled state there exists a fixed one-way LOCC measurement that distinguishes it from any separable state with error probability that decays exponentially in n.Comment: v2: 43 pages, 5 figures, completely rewritten and in Theory of Computing (ToC) journal forma

Increasing the voluntary and community sector’s involvement in Integrated Offender Management(IOM)

As part of an undertaking to increase voluntary and community sector (VCS) involvement in service delivery, the Home Office set up an initiative to provide small grants to VCS organisations to work with IOM partnerships. The Home Office commissioned an evaluation of the initiative which aimed to: explore the strengths and weaknesses of the funding model; identify perceived barriers and facilitators to voluntary and community sector involvement in IOM; explore how the Home Office might best work with the VCS to encourage and support their capacity to work in partnership with statutory agencies; and identify any implications for the delivery of future similar projects

Process evaluation of Derbyshire Intensive Alternatives to Custody Pilot

The aim of this study was to critically assess the implementation and development of the Intensive Alternatives to Custody (IAC) pilot in Derbyshire. The Ministry of Justice (MoJ) Penal Policy paper (May 2007) outlined the government’s intention to develop higher intensity community orders as an alternative to short-term custody. The IAC Order was subsequently developed and piloted, first in Derbyshire and then in six other areas.* The pilots were centrally funded until March 2011

Robotics Research with Turtlebot 2016

A Turtlebot robot platform is being used for robotics and computer vision research at Boise State. Turtlebot is an open­source robotics platform controlled by the ROS (Robot Operating System) framework. This semester we are developing capabilities for the robot to participate in the Boise State Easter Egg Hunt, an event for children on the blue turf. The broad steps include: a) retro­fit Turtlebot with a small motor­controlled egg scooper, b) use Turtlebot’s vision hardware to identify and locate eggs and c) navigate to and pick up located egg(s). The team used 3D modelling and printing techniques to retro­fit Turtlebot with a motorized scooper controlled by an Arduino UNO and equipped with sensors. Computer vision capabilities were integrated with ROS through OpenCV Python to analyze the Kinect’s video data. Frames from the Kinect video stream were modified to minimize noise while preserving features. Frames are searched to find circular clusters of white pixels (the eggs). After a target egg is chosen, Turtlebot moves towards the egg and captures it with the scoop. Through SLAM (Simultaneous Localization and Mapping), Turtlebot navigates back to its predetermined “Home” location. We utilize slow speeds and object avoidance to ensure Turtlebot was also kid­friendl

Cassini atmospheric chemistry mapper. Volume 1. Investigation and technical plan

The Cassini Atmospheric Chemistry Mapper (ACM) enables a broad range of atmospheric science investigations for Saturn and Titan by providing high spectral and spatial resolution mapping and occultation capabilities at 3 and 5 microns. ACM can directly address the major atmospheric science objectives for Saturn and for Titan, as defined by the Announcement of Opportunity, with pivotal diagnostic measurements not accessible to any other proposed Cassini instrument. ACM determines mixing ratios for atmospheric molecules from spectral line profiles for an important and extensive volume of the atmosphere of Saturn (and Jupiter). Spatial and vertical profiles of disequilibrium species abundances define Saturn's deep atmosphere, its chemistry, and its vertical transport phenomena. ACM spectral maps provide a unique means to interpret atmospheric conditions in the deep (approximately 1000 bar) atmosphere of Saturn. Deep chemistry and vertical transport is inferred from the vertical and horizontal distribution of a series of disequilibrium species. Solar occultations provide a method to bridge the altitude range in Saturn's (and Titan's) atmosphere that is not accessible to radio science, thermal infrared, and UV spectroscopy with temperature measurements to plus or minus 2K from the analysis of molecular line ratios and to attain an high sensitivity for low-abundance chemical species in the very large column densities that may be achieved during occultations for Saturn. For Titan, ACM solar occultations yield very well resolved (1/6 scale height) vertical mixing ratios column abundances for atmospheric molecular constituents. Occultations also provide for detecting abundant species very high in the upper atmosphere, while at greater depths, detecting the isotopes of C and O, constraining the production mechanisms, and/or sources for the above species. ACM measures the vertical and horizontal distribution of aerosols via their opacity at 3 microns and, particularly, at 5 microns. ACM recovers spatially-resolved atmospheric temperatures in Titan's troposphere via 3- and 5-microns spectral transitions. Together, the mixing ratio profiles and the aerosol distributions are utilized to investigate the photochemistry of the stratosphere and consequent formation processes for aerosols. Finally, ring opacities, observed during solar occultations and in reflected sunlight, provide a measurement of the particle size and distribution of ring material. ACM will be the first high spectral resolution mapping spectrometer on an outer planet mission for atmospheric studies while retaining a high resolution spatial mapping capability. ACM, thus, opens an entirely new range of orbital scientific studies of the origin, physio-chemical evolution and structure of the Saturn and Titan atmospheres. ACM provides high angular resolution spectral maps, viewing nadir and near-limb thermal radiation and reflected sunlight; sounds planetary limbs, spatially resolving vertical profiles to several atmospheric scale heights; and measures solar occultations, mapping both atmospheres and rings. ACM's high spectral and spatial resolution mapping capability is achieved with a simplified Fourier Transform spectrometer with a no-moving parts, physically compact design. ACM's simplicity guarantees an inherent stability essential for reliable performance throughout the lengthy Cassini Orbiter mission

Gene Flow in Complex Landscapes: Testing Multiple Hypotheses with Causal Modeling.

Predicting population-level effects of landscape change depends on identifying factors that influence population connectivity in complex landscapes. However, most putative movement corridors and barriers have not been based on empirical data. In this study, we identify factors that influence connectivity by comparing patterns of genetic similarity among 146 black bears (Ursus americanus), sampled across a 3,000-km2 study area in northern Idaho, with 110 landscape-resistance hypotheses. Genetic similarities were based on the pairwise percentage dissimilarity among all individuals based on nine microsatellite loci (average expected heterozygosityp0.79). Landscape-resistance hypotheses describe a range of potential relationships between movement cost and land cover, slope, elevation, roads, Euclidean distance, and a putative movement barrier. These hypotheses were divided into seven organizational models in which the influences of barriers, distance, and landscape features were statistically separated using partial Mantel tests. Only one of the competing organizational models was fully supported: patterns of genetic structure are primarily related to landscape gradients of land cover and elevation. The alternative landscape models, isolation by barriers and isolation by distance, are not supported. In this black bear population, gene flow is facilitated by contiguous forest cover at middle elevations

Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations

Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing. In this way the approximating solution is coupled to the reference solution at a discrete sequence of points in time. This paper studies discrete data assimilation for the Lorenz equations and the incompressible two-dimensional Navier--Stokes equations. In both cases we obtain bounds on the time interval h between subsequent observations which guarantee the convergence of the approximating solution obtained by discrete data assimilation to the reference solution

Incorporating Search and Sales Information in Demand Estimation

We propose an approach to modeling and estimating discrete choice demand that allows for a large number of zero sale observations, rich unobserved heterogeneity, and endogenous prices. We do so by modeling small market sizes through Poisson arrivals. Each of these arriving consumers then solves a standard discrete choice problem. We present a Bayesian IV estimation approach that addresses sampling error in product shares and scales well to rich data environments. The data requirements are traditional market-level data and measures of consumer search intensity. After presenting simulation studies, we consider an empirical application of air travel demand where product-level sales are sparse. We find considerable variation in demand over time. Periods of peak demand feature both larger market sizes and consumers with higher willingness to pay. This amplifies cyclicality. However, observed frequent price and capacity adjustments offset some of this compounding effect