Maximization of capacity and p-norms for some product channels

It is conjectured that the Holevo capacity of a product channel \Omega \otimes \Phi is achieved when product states are used as input. Amosov, Holevo and Werner have also conjectured that the maximal p-norm of a product channel is achieved with product input states. In this paper we establish both of these conjectures in the case that \Omega is arbitrary and \Phi is a CQ or QC channel (as defined by Holevo). We also establish the Amosov, Holevo and Werner conjecture when \Omega is arbitrary and either \Phi is a qubit channel and p=2, or \Phi is a unital qubit channel and p is integer. Our proofs involve a new conjecture for the norm of an output state of the half-noisy channel I \otimes \Phi, when \Phi is a qubit channel. We show that this conjecture in some cases also implies additivity of the Holevo capacity

Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2

We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go beyond p>2 and obtain additivity for p=0 for a class of entanglement breaking channels.Comment: 4 pages; a reference adde

Age structure, dispersion and diet of a population of stoats (Mustela erminea) in southern Fiordland during the decline phase of the beechmast cycle

The dispersion, age structure and diet of stoats (Mustela erminea) in beech forest in the Borland and Grebe Valleys, Fiordland National Park, were examined during December and January 2000/01, 20 months after a heavy seed-fall in 1999. Thirty trap stations were set along a 38-km transect through almost continuous beech forest, at least 1 km apart. Mice were very scarce (nights, C/100TN) along two standard index lines placed at either end of the transect, compared with November 1999 (>60/100TN), but mice were detected (from footprints in stoat tunnels) along an 8 km central section of the transect (stations 14-22). Live trapping with one trap per station (total 317.5 trap nights) in December 2000 caught 2 female and 23 male stoats, of which 10 (including both females) were radio collared. The minimum range lengths of the two females along the transect represented by the trap line were 2.2 and 6.0 km; those of eight radio-tracked males averaged 2.9 ± 1.7 km. Stations 14-22 tended to be visited more often, by more marked individual stoats, than the other 21 stations. Fenn trapping at the same 30 sites, but with multiple traps per station (1333.5 trap nights), in late January 2001 collected carcasses of 35 males and 28 females (including 12 of the marked live-trapped ones). Another two marked males were recovered dead. The stoat population showed no sign of chronic nutritional stress (average fat reserve index = 2.8 on a scale of 1-4 where 4 = highest fat content); and only one of 63 guts analysed was empty. Nevertheless, all 76 stoats handled were adults with 1-3 cementum annuli in their teeth, showing that reproduction had failed that season. Prey categories recorded in descending frequency of occurrence were birds, carabid beetle (ground beetle), weta, possum, rat, and mouse. The frequencies of occurrence of mice and birds in the diet of these stoats (10% and 48%, respectively) were quite different from those in stoats collected in Pig Creek, a tributary of the Borland River (87%, 5%), 12 months previously when mice were still abundant. Five of the six stoat guts containing mice were collected within 1 km of stations 14-22

Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions

Entropy reduction of quantum measurements

It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori state to the corresponding posteriori probability distribution of the outcomes of the measurement. This observation makes it possible to define the entropy reduction for arbitrary a priori states (not only for states with finite von Neumann entropy) and to study its analytical properties by using general properties of the quantum mutual information. By using this approach one can show that the entropy reduction of an efficient quantum measurement is a nonnegative lower semicontinuous concave function on the set of all a priori states having continuous restrictions to subsets on which the von Neumann entropy is continuous. Monotonicity and subadditivity of the entropy reduction are also easily proved by this method. A simple continuity condition for the entropy reduction and for the mean posteriori entropy considered as functions of a pair (a priori state, measurement) is obtained. A characterization of an irreducible measurement (in the Ozawa sense) which is not efficient is considered in the Appendix.Comment: 21 pages, minor corrections have been mad

Black Widow Pulsars: the Price of Promiscuity

The incidence of evaporating 'black widow' pulsars (BWPs) among all millisecond pulsars (MSPs) is far higher in globular clusters than in the field. This implies a special formation mechanism for them in clusters. Cluster MSPs in wide binaries with WD companions exchange them for turnoff-mass stars. These new companions eventually overflow their Roche lobes because of encounters and tides. The millisecond pulsars eject the overflowing gas from the binary, giving mass loss on the binary evolution timescale. The systems are only observable as BWPs at epochs where this evolution is slow, making the mass loss transparent and the lifetime long. This explains why observed BWPs have low-mass companions. We suggest that at least some field BWPs were ejected from globular clusters or entered the field population when the cluster itself was disrupted.Comment: 6 pages, 2 figures, MNRAS in pres

Qubit Channels Can Require More Than Two Inputs to Achieve Capacity

We give examples of qubit channels that require three input states in order to achieve the Holevo capacity.Comment: RevTex, 5 page, 4 figures

The tension between fire risk and carbon storage: evaluating U.S. carbon and fire management strategies through ecosystem models

Fire risk and carbon storage are related environmental issues because fire reduction results in carbon storage through the buildup of woody vegetation, and stored carbon is a fuel for fires. The sustainability of the U.S. carbon sink and the extent of fire activity in the next 100 yr depend in part on the type and effectiveness of fire reduction employed. Previous studies have bracketed the range of dynamics from continued fire reduction to the complete failure of fire reduction activities. To improve these estimates, it is necessary to explicitly account for fire reduction in terrestrial models. A new fire reduction submodel that estimates the spatiotemporal pattern of reduction across the United States was developed using gridded data on biomass, climate, land-use, population, and economic factors. To the authors’ knowledge, it is the first large-scale, gridded fire model that explicitly accounts for fire reduction. The model was calibrated to 1° × 1° burned area statistics [Global Burnt Area 2000 Project (GBA-2000)] and compared favorably to three important diagnostics. The model was then implemented in a spatially explicit ecosystem model and used to analyze 1620 scenarios of future fire risk and fire reduction strategies. Under scenarios of climate change and urbanization, burned area and carbon emissions both increased in scenarios where fire reduction efforts were not adjusted to match new patterns of fire risk. Fuel reducing management strategies reduced burned area and fire risk, but also limited carbon storage. These results suggest that to promote carbon storage and minimize fire risk in the future, fire reduction efforts will need to be increased and spatially adjusted and will need to employ a mixture of fuel-reducing and non-fuel-reducing strategies