Recovering full coherence in a qubit by measuring half of its environment

When quantum systems interact with the environment they lose their quantum properties, such as coherence. Quantum erasure makes it possible to restore coherence in a system by measuring its environment, but accessing the whole of it may be prohibitive: realistically one might have to concentrate only on an accessible subspace and neglect the rest. If that is the case, how good is quantum erasure? In this work we compute the largest coherence $\langle \mathcal C\rangle$ that we can expect to recover in a qubit, as a function of the dimension of the accessible and of the inaccessible subspaces of its environment. We then imagine the following game: we are given a uniformly random pure state of $n+1$ qubits and we are asked to compute the largest coherence that we can retrieve on one of them by optimally measuring a certain number $0\leq a\leq n$ of the others. We find a surprising effect around the value $a\approx n/2$: the recoverable coherence sharply transitions between 0 and 1, indicating that in order to restore full coherence on a qubit we need access to only half of its physical environment (or in terms of degrees of freedom to just the square root of them). Moreover, we find that the recoverable coherence becomes a typical property of the whole ensemble as $n$ grows.Comment: 4 pages, 5 figure

Controls on dissolved organic carbon quantity and chemical character in temperate rivers of North America

Understanding the processes controlling the transfer and chemical composition of dissolved organic carbon (DOC) in freshwater systems is crucial to understanding the carbon cycle and the effects of DOC on water quality. Previous studies have identified watershed‐scale controls on bulk DOC flux and concentration among small basins but fewer studies have explored controls among large basins or simultaneously considered the chemical composition of DOC. Because the chemical character of DOC drives riverine biogeochemical processes such as metabolism and photodegradation, accounting for chemical character in watershed‐scale studies will improve the way bulk DOC variability in rivers is interpreted. We analyzed DOC quantity and chemical character near the mouths of 17 large North American rivers, primarily between 2008 and 2010, and identified watershed characteristics that controlled variability. We quantified DOC chemical character using both specific ultraviolet absorbance at 254 nm (SUVA254) and XAD‐resin fractionation. Mean DOC concentration ranged from 2.1 to 47 mg C L−1 and mean SUVA254 ranged from 1.3 to 4.7 L mg C−1 m−1. We found a significant positive correlation between basin wetland cover and both bulk DOC concentration (R2 = 0.78; p \u3c 0.0001) and SUVA254 (R2 = 0.91; p \u3c 0.0001), while other land use characteristics were not correlated. The strong wetland relationship with bulk DOC concentration is similar to that found by others in small headwater catchments. However, two watersheds with extremely long surface water residence times, the Colorado and St. Lawrence, diverged from this wetland relationship. These results suggest that the role of riverine processes in altering the terrestrial DOC signal at the annual scale was minimal except in river systems with long surface water residence times. However, synoptic DOC sampling of both quantity and character throughout river networks will be needed to more rigorously test this finding. The inclusion of DOC chemical character will be vital to achieving a more complete understanding of bulk DOC dynamics in large river systems

Elliptic Reciprocity

The paper introduces the notions of an elliptic pair, an elliptic cycle and an elliptic list over a square free positive integer d. These concepts are related to the notions of amicable pairs of primes and aliquot cycles that were introduced by Silverman and Stange. Settling a matter left open by Silverman and Stange it is shown that for d=3 there are elliptic cycles of length 6. For d not equal to 3 the question of the existence of proper elliptic lists of length n over d is reduced to the the theory of prime producing quadratic polynomials. For d=163 a proper elliptic list of length 40 is exhibited. It is shown that for each d there is an upper bound on the length of a proper elliptic list over d. The final section of the paper contains heuristic arguments supporting conjectured asymptotics for the number of elliptic pairs below integer X. Finally, for d congruent to 3 modulo 8 the existence of infinitely many anomalous prime numbers is derived from Bunyakowski's Conjecture for quadratic polynomials.Comment: 17 pages, including one figure and two table

Nonproductive Events in Ring-Closing Metathesis Using Ruthenium Catalysts

The relative TONs of productive and nonproductive metathesis reactions of diethyl diallylmalonate are compared for eight different ruthenium-based catalysts. Nonproductive cross metathesis is proposed to involve a chain-carrying ruthenium methylidene. A second more-challenging substrate (dimethyl allylmethylallylmalonate) that forms a trisubstituted olefin product is used to further delineate the effect of catalyst structure on the relative efficiencies of these processes. A steric model is proposed to explain the observed trends

Method Effects and the Need for Cognition Scale

Individual differences in the need for cognition are typically assessed using the 18-item Need for cognition scale (NCS) developed by Cacioppo and Petty (1982). However, in contrast to the unidimensional model proposed by the scale developers, recent factor analyses have introduced two -and three- dimensional models of the scale. Confirmatory factor analyses were used in this study to evaluate different measurement models based on data provided by 590 (236 males, 354 females) young adult members of the general public. Although some alternative models showed promise, a single factor model with method effects associated with positively and negatively worded items provided best fit. Implications for the asses sment of need for cognition are considered

Algebraic properties of generalized Rijndael-like ciphers

We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field \GF (p^k) ($p\geq 2$ a prime number) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen the AES (Rijndael block cipher with specific block sizes) in case AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (2^k) is equal to the alternating group on the state space. In this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (p^k) ($p\geq 2$) is equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0