Splittings of groups and intersection numbers

We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple curve, and that two simple curves on a surface with intersection number zero can be isotoped to be disjoint.Comment: 40 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper6.abs.htm

Local and global statistical distances are equivalent on pure states

The statistical distance between pure quantum states is obtained by finding a measurement that is optimal in a sense defined by Wootters. As such, one may expect that the statistical distance will turn out to be different if the set of possible measurements is restricted in some way. It nonetheless turns out that if the restriction is to local operations and classical communication (LOCC) on any multipartite system, then the statistical distance is the same as it is without restriction, being equal to the angle between the states in Hilbert space.Comment: 5 pages, comments welcom

Holidaying with the family pet: No dogs allowed!

This paper assesses the extent to which dog owners located in Brisbane, Australia, wish to holiday with their pets, and whether there is a gap between this desire and reality. The paper also examines the extent to which this demand is being catered for by the tourism accommodation sector. The need for this study reflects the increasingly significant role dogs are playing in the lives of humans, and the scale of the dog-owning population. The results suggest that, although there is a strong desire among dog owners to take holidays with their pets, the actualisation of this desire is comparatively low. A significant obstacle to the realisation of this desire appears to be a dearth of pet-friendly accommodation. This has implications for the ability of the tourism industry to benefit from this potentially lucrative market, that is, the dog-owning population

Atemporal diagrams for quantum circuits

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using PSTrick

Women's Work and European Fertility Patterns

http://deepblue.lib.umich.edu/bitstream/2027.42/50872/1/95.pd

Rethinking Visiting Friends and Relatives Mobilities

The increasing number of people leading more mobile lives, with spatially dispersed families, raises questions over how they maintain their family life and friendships, and how this is shaped and shapes different forms of migration, and different patterns of Visiting Friends and Relatives (VFR). This paper develops an explanatory framework for conceptualizing and analyzing VFR mobilities, seeking to draw together threads from migration, mobilities and tourism studies. In unpacking the notion of VFR, this paper understands VFR mobilities as being constituted of diverse practices, and discusses five of the most important of these: social relationships, the provision of care, affirmations of identities and roots, maintenance of territorial rights, and leisure tourism. While these five types of practices are considered sequentially in this paper, they are in practice often blurred and overlapping. The interweaving of these practices changes over time, as does the meaning and content of individual practices, reflecting changes in the duration of migration, life cycle stage, individual goals and values, and the broader sets of relationships with and social obligations to different kin and friends

Spectral structure near the 11.3 micron emission feature

If the 11.3 micron emission feature seen in the spectra of many planetary nebulae, H II regions, and reflection nebulae is attributable to polycyclic aromatic hydrocarbons (PAHs), then additional features should be present between 11.3 and 13.0 microns. Moderate resolution spectra of NGC 7027, HD 44179, BD+30 deg 3639, and IRAS 21282+5050 are presented which show evidence for new emission features centered near 12.0 and 12.7 microns. These are consistent with an origin from PAHs and can be used to constrain the molecular structure of the family of PAHs responsible for the infrared features. There is an indication that coronene-like PAHs contribute far more to the emission from NGC 7027 than to the emission from HD 44179. The observed asymmetric profile of the 11.3 micron band in all the spectra is consistent with the slight anharmonicity expected in the C-H out-of-plane bending mode in PAHs. A series of repeating features between 10 and 11 microns in the spectrum of HD 44179 suggests a simple hydride larger than 2 atoms is present in the gas phase in this object

Deterministic and Unambiguous Dense Coding

Optimal dense coding using a partially-entangled pure state of Schmidt rank $\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in the deterministic case where at most $L_d$ messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability $\tau_x$) Bob knows for sure that Alice sent message $x$, and when it fails (probability $1-\tau_x$) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For $\bar D\leq D$ a bound is obtained for $L_d$ in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. For $\bar D > D$ it is shown that $L_d$ is strictly less than $D^2$ unless $\bar D$ is an integer multiple of $D$, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for $\bar D \leq D$, assuming $\tau_x>0$ for a set of $\bar D D$ messages, and a bound is obtained for the average \lgl1/\tau\rgl. A bound on the average \lgl\tau\rgl requires an additional assumption of encoding by isometries (unitaries when $\bar D=D$) that are orthogonal for different messages. Both bounds are saturated when $\tau_x$ is a constant independent of $x$, by a protocol based on one-shot entanglement concentration. For $\bar D > D$ it is shown that (at least) $D^2$ messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states.Comment: Short new section VII added. Latex 23 pages, 1 PSTricks figure in tex

Local cloning of entangled states

We investigate the conditions under which a set \SC of pure bipartite quantum states on a $D\times D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in \SC must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set \SC can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit states with non-vanishing entanglement. In both of these cases, a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary "shift" operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in D=3 we show that a maximally entangled resource is again necessary and sufficient, while for higher dimensional systems, we find that the resource state must be strictly more entangled than the states in \SC. All of our necessary conditions for separable operations are also necessary conditions for LOCC, since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.Comment: REVTEX 15 pages, 1 figure, minor modifications. Same as the published version. Any comments are welcome