Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers

We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.Comment: 18 pages, 15 figures, submitted to Proc. R. Soc.

Structured Error Recovery for Codeword-Stabilized Quantum Codes

Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. In this paper, we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3^t times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.Comment: 13 pages, 9 eps figure

Multiparticle entanglement purification for graph states

We introduce a class of multiparticle entanglement purification protocols that allow us to distill a large class of entangled states. These include cluster states, GHZ states and various error correction codes all of which belong to the class of two-colorable graph states. We analyze these schemes under realistic conditions and observe that they are scalable, i.e. the threshold value for imperfect local operations does not depend on the number of parties for many of these states. When compared to schemes based on bipartite entanglement purification, the protocol is more efficient and the achievable quality of the purified states is larger. As an application we discuss an experimental realization of the protocol in optical lattices which allows one to purify cluster states.Comment: 4 pages, 2 figures; V2: some typos corrected; V3: published versio

On local invariants of pure three-qubit states

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree less than or equal to 6, and find such a set with maximum degree 8. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.Comment: LateX, 13 pages. Minor typoes corrected. Published versio

Relationship between clear-sky atmospheric greenhouse effect and deep convection during the Central Equatorial Pacific Experiment: Model calculations and satellite observations

This study investigates the relation between tropical convection and the atmospheric greenhouse effect using data collected during the Central Equatorial Pacific Experiment (CEPEX). We present calculations of total clear-sky greenhouse effect and its partitioning between the lower, middle, and upper troposphere using high-quality balloon soundings of temperature and humidity as input to a radiative transfer model. The soundings were taken from a ship every 6 hours from March 7 to 20, 1993, in the central Pacific. We examine the influence on atmospheric greenhouse effect due to changes in humidity and lapse rate and investigate the relationship between atmospheric greenhouse effect, water vapor, and deep convection. Our observations indicate that periods of active or suppressed convection with timescales of the order of days can produce large spatial gradients in clear-sky atmospheric greenhouse trapping in warm, climatologically convective regions. While the sea surface temperature (SST) decreased by 2 K from west to east, temperatures above 850 mbar showed considerably less variation. Accordingly, lapse rate changes occurred primarily in the boundary layer and such changes account for 80% of the gradient in boundary layer greenhouse effect. The column-integrated water vapor content from the surface to 850 mbar was nearly constant in each of the regimes. Conversely, large variations in column-integrated water vapor above 850 mbar and particularly above 500 mbar account for nearly all the gradient in the greenhouse effect in the middle and upper troposphere. Coincident outgoing longwave radiation (OLR) analyses derived from satellite observations show active deep convection in areas with high clear-sky greenhouse trapping and upper level moisture and generally clear, suppressed conditions elsewhere. In addition, the surface net flux and outgoing flux emitted to space decreased with increased SST. The reduced cooling of the ocean-atmosphere system is consistent with a supergreenhouse effect operating in regions of deep convection

Block synchronization for quantum information

Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries of quantum information without relying on external synchronization when block synchronization is lost. The method also protects qubits from decoherence in a manner similar to conventional quantum error-correcting codes, seamlessly achieving synchronization recovery and error correction. A family of quantum codes that are simultaneously synchronizable and error-correcting is given through this approach.Comment: 7 pages, no figures, final accepted version for publication in Physical Review

Generalized Concatenation for Quantum Codes

We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both stabilizer codes as well as so-called nonadditive codes.Comment: 5 pages, to be presented at ISIT 200

On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature

Satellite infrared sensors only observe the temperature of the skin of the ocean rather than the bulk sea surface temperature (SST) traditionally measured from ships and buoys. In order to examine the differences and similarities between skin and bulk temperatures, radiometric measurements of skin temperature were made in the North Atlantic Ocean from a research vessel along with coincident measurements of subsurface bulk temperatures, radiative fluxes, and meteorological variables. Over the entire 6-week data set the bulk-skin temperature differences (AT) range between -1.0 and 1.0 K with mean differences of 0.1 to 0.2 K depending on wind and surface heat flux conditions. The bulk-skin temperature difference varied between day and night (mean differences 0.11 and 0.30 K, respectively) as well as with different cloud conditions, which can mask the horizontal variability of SST in regions of weak horizontal temperature gradients. A coherency analysis reveals strong correlations between skin and bulk temperatures at longer length scales in regions with relatively weak horizontal temperature gradients. The skin-bulk temperature difference is pararneterized in terms of heat and momentum fluxes (or their related variables) with a resulting accuracy of 0.11 K and 0.17 K for night and daytime. A recommendation is made to calibrate satellite derived SST's during night with buoy measurements and the additional aid of meteorological variables to properly handle AT variations

Multiparticle entanglement purification for two-colorable graph states

We investigate multiparticle entanglement purification schemes which allow one to purify all two colorable graph states, a class of states which includes e.g. cluster states, GHZ states and codewords of various error correction codes. The schemes include both recurrence protocols and hashing protocols. We analyze these schemes under realistic conditions and observe for a generic error model that the threshold value for imperfect local operations depends on the structure of the corresponding interaction graph, but is otherwise independent of the number of parties. The qualitative behavior can be understood from an analytically solvable model which deals only with a restricted class of errors. We compare direct multiparticle entanglement purification protocols with schemes based on bipartite entanglement purification and show that the direct multiparticle entanglement purification is more efficient and the achievable fidelity of the purified states is larger. We also show that the purification protocol allows one to produce private entanglement, an important aspect when using the produced entangled states for secure applications. Finally we discuss an experimental realization of a multiparty purification protocol in optical lattices which is issued to improve the fidelity of cluster states created in such systems.Comment: 22 pages, 8 figures; replaced with published versio

Comparison of satellite-derived sea surface temperatures with in situ skin measurements

Sea surface temperatures (SSTs), computed from sensor systems on the National Oceanographic and Atmospheric Administration (NOAA) polar-orbiting satellites, are compared with surface skin temperatures (from an infrared radiometer mounted on a ship) and subsurface temperature measurements. Three split window retrieval methods using channels 4 and 5 of the NOAA 7 advanced very high resolution radiometer (AVHRR) sensor were investigated. These methods were (1) using AVHRR alone, (2) using AVHRR with atmospheric temperature and water vapor profiles from the TIROS operational vertical sounder (TOVS), and (3) using AVHRR and data from the high-resolution infrared sounder (HIRS). TOVS sensors (including HIRS) are carried by the same satellite as the AVHRR and provide simultaneous corrections for the AVHRR-based SST estimates. The importance of scan angle correction to define the correct atmospheric path is discussed, and the improvement of SST retrievals using sensor combinations is demonstrated with satellite versus ship skin temperature mean differences ranging from 0.55° to 0.73°C for AVHRR alone, from -0.39°to 0.71°C for AVHRR plus TOVS, and from 0.22°to 0.33°C for AVHRR plus HIRS. The improved SST accuracy by AVHRR plus HIRS is due to additional correction for the atmospheric water vapor and temperature structures, made possible with some of the HIRS channels. Significant differences between ship skin and subsurface temperatures were observed, with the mean deviation being 0.2°C for a range of temperature differences between -0.25°and 0.6°C. © Copyright 1987 by the American Geophysical Union