Structured Near-Optimal Channel-Adapted Quantum Error Correction

We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace preserving (CPTP) constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality.Comment: 18 pages, 13 figures Update: typos corrected in Appendi

Effects of sinking velocities and microbial respiration rates on the attenuation of particulate carbon fluxes through the mesopelagic zone

Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 29 (2015): 175–193, doi:10.1002/2014GB004935.The attenuation of sinking particle fluxes through the mesopelagic zone is an important process that controls the sequestration of carbon and the distribution of other elements throughout the oceans. Case studies at two contrasting sites, the oligotrophic regime of the Bermuda Atlantic Time-series Study (BATS) and the mesotrophic waters of the west Antarctic Peninsula (WAP) sector of the Southern Ocean, revealed large differences in the rates of particle-attached microbial respiration and the average sinking velocities of marine particles, two parameters that affect the transfer efficiency of particulate matter from the base of the euphotic zone into the deep ocean. Rapid average sinking velocities of 270 ± 150 m d−1 were observed along the WAP, whereas the average velocity was 49 ± 25 m d−1 at the BATS site. Respiration rates of particle-attached microbes were measured using novel RESPIRE (REspiration of Sinking Particles In the subsuRface ocEan) sediment traps that first intercepts sinking particles then incubates them in situ. RESPIRE experiments yielded flux-normalized respiration rates of 0.4 ± 0.1 day−1 at BATS when excluding an outlier of 1.52 day−1, while these rates were undetectable along the WAP (0.01 ± 0.02 day−1). At BATS, flux-normalized respiration rates decreased exponentially with respect to depth below the euphotic zone with a 75% reduction between the 150 and 500 m depths. These findings provide quantitative and mechanistic insights into the processes that control the transfer efficiency of particle flux through the mesopelagic and its variability throughout the global oceans.Funding was provided by the University of Alaska Fairbanks, Woods Hole Oceanographic Institution (WHOI) Rinehart Access to the Sea Program, the WHOI Coastal Oceans Institute, WHOI Academic Programs Office, and the National Science Foundation (NSF) for support of PAL (ANT-0823101), FOODBANCS, and WAPflux (ANT- 83886600) projects. A grant from the NSF Carbon and Water Program (06028416) supported the development of these methods.2015-08-2

Precision spectroscopy and density-dependent frequency shifts in ultracold Sr

By varying the density of an ultracold $^{88}$Sr sample from $10^9$ cm$^{-3}$ to $> 10^{12}$ cm$^{-3}$, we make the first definitive measurement of the density-related frequency shift and linewidth broadening of the $^1S_0$ - $^3P_1$ optical clock transition in an alkaline earth system. In addition, we report the most accurate measurement to date of the $^{88}$Sr $^1S_0 - ^3P_1$ optical clock transition frequency. Including a detailed analysis of systematic errors, the frequency is ($434 829 121 312 334 \pm 20_{stat} \pm 33_{sys}$) Hz.Comment: 4 pages, 4 figures, 1 table. submitte

Application of the Transition Probability Matrix Method to High Knudsen Number Flow Past a Micro‐Plate

In this work we present numerical results for the problem of ‘high’ (of order unity) Knudsen number gas flow past a micro‐airfoil, for low flow velocity. The results are generated using an enhanced version of the transition probability matrix (TPM) method. The TPM is a non‐statistical kinetic method [1] for computing neutral particle transport in high Knudsen number flows. The problem of high Knudsen number, low Mach number gas flow has been studied in the past using several computational approaches, such as the Information Preservation (IP) method [2] and the direct simulation Monte Carlo (DSMC) method [2]. For low Mach numbers, the DSMC approach suffers from statistical noise [3]. The IP method extends the range of the particle method by reducing the statistical noise of the approach. The need for a method which is capable of describing the particle distribution function for high Knudsen number flows at low flow velocities has led to an investigation of alternative kinetic approaches, such as the IP[4]. In this paper we present an altogether different approach to the problem of statistical noise, the transition probability matrix (TPM) method [1, 5, 6, 7]. We give a brief overview of the TPM method, and compare its strengths and weaknesses to those of the IP and DSMC methods. Finally, we present results for the micro‐plate and compare them to the results generated by both the IP and DSMC methods. © 2003 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87934/2/768_1.pd

Better Bell Inequality Violation by Collective Measurements

The standard Bell inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.Comment: 7 pages, 4 figures and 1 table; references update

The Glaciochemistry of Snowpits from Quelccaya Ice Cap, Peru, 1982

We present glaciochemical data from a pilot study of two snow-pits from Quelccaya ice cap, Peruvian Andes. These are the first samples to be analyzed from Quelccaya for nitrate and sulfate by ion chromatography (IC), for nitrate-plus-nitrite, reactive silicate and reactive iron by colorimetry, and for sodium by atomic absorption spectrophotometry. The 3 m pits used in this study represent a one year record of mass accumulation and the 29 samples collected provide the first glaciochemical data from this area which can be compared with glaciochemical studies from other locations. Reactive iron, reactive silicate and sodium, and the profiles of \u3e0.63µm microparticles from Thompson and others (1984) are coincident, suggesting that transport and deposition into this area of each species are controlled by similar processes. The common source is probably local, resulting from crustaI weathering. In general, the reactive silicate values are lower than those observed in other alpine glacier ice. The highest sulfate and nitrate values were observed in the upper few centimeters of the snow-pit. Most of the sulfate concentrations were less than 3 µM and are similar to values obtained for fresh surface snows from Bolivia (Stallard and Edmond 1981). Since biological gaseous emissions are thought to be the major source of sulfur and nitrogen to the atmosphere over the Amazon basin, the sulfate and nitrate fluctuations may be due to seasonal biological input and/or seasonal shifts in wind direction bringing material to Quelccaya. With only one exception, the colorimetric nitrate-plus-nitrite data were higher than the IC nitrate data. Unfortunately, the IC analyses were conducted 81 d after the colorimetric analyses. The difference between the two data sets could be attributable to the following; (I) the colorimetric technique may yield erroneously high results as suggested for polar ice by Herron (1982), (2) the IC technique yields erroneously low results due, in part, to the possible exclusion of nitrite concentrations, and/or (3) nitrite was lost via biological removal during the 81 d period before the IC analyses. If the IC data are correct, the mean nitrate value is O.4 µM (n = 29). This value is similar to those reported from pre-industrial aged polar ice (Herron 1982). If the colorimetric mean value (1.1 µM) is correct, it is similar to colorimetrically determined values from other high-elevation alpine ice (Lyons and Mayewski 1983)

Glaciochemical Studies and Estimated Net Mass Balances for Rennick Glacier Area, Antarctica

Two snow and ice cores from the Rennick Glacier area, Antarctica (study area center point lat 71° 15\u27 S, long 162° 30\u27 E) were analyzed for the chemical species: chloride, sodium, reactive silicate, sulfate and nitrate. Core E1O (6.35 m) was taken from Evans Névé, a large accumulation basin at the head of Rennick Glacier. Core M1 (4.35 m) was extracted from the accumulation zone on the central plateau of the Morozumi Range, a small mountain massif bordering Rennick Glacier. Cores E1O and M1 span the time periods from 1929 to 1981 and from 1971 to 1981, respectively, as dated using seasonal variations in chloride (E10) and sulfate (M1) concentrations. An estimated net balance of 50 kg m-2 a-1 was derived for site E10 and of 182 kg m- 2 a-I for site Ml. The difference in net mass balance may be explained by elevational differences (M1 1400 m a.s.l., E1O 2305 m a.s.l .). Recent (1973 to 1980) increases in sodium, silicate and sulfate at site E1O may be linked to decreases in Antarctic pack-ice extent (Kukla and Gavin 1981) for the same period

Quantum-limited estimation of the axial separation of two incoherent point sources

Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cram\'er-Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require neither activation of fluorophores nor sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful to a variety of applications such as far-field fluorescence microscopy.Comment: Comments are welcom

Colloquium: Understanding Quantum Weak Values: Basics and Applications

Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation for how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a measurable complex value it enables novel techniques for direct quantum state and geometric phase determination. Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In this selective review, a single experimental configuration to discuss and clarify each of these applications is used.Comment: 11 pages, 5 figures, published versio