The Power of LOCCq State Transformations

Reversible state transformations under entanglement non-increasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end \cite{BPRST01} have defined more powerful versions of state transformations (or reducibilities), namely LOCCq (asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC (asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state transformations are only as powerful as asymptotic LOCC state transformations} for multipartite pure states. We first generalize the concept of entanglement gambling from two parties to multiple parties: any pure multipartite entangled state can be transformed to an EPR pair shared by some pair of parties and that any irreducible $m$ $(m\ge 2)$ party pure state can be used to create any other state (pure or mixed), using only local operations and classical communication (LOCC). We then use this tool to prove the result. We mention some applications of multipartite entanglement gambling to multipartite distillability and to characterizations of multipartite minimal entanglement generating sets. Finally we discuss generalizations of this result to mixed states by defining the class of {\em cat distillable states}

The PLC: a logical development

Programmable Logic Controllers (PLCs) have been used to control industrial processes and equipment for over 40 years, having their first commercially recognised application in 1969. Since then there have been enormous changes in the design and application of PLCs, yet developments were evolutionary rather than radical. The flexibility of the PLC does not confine it to industrial use and it has been used for disparate non-industrial control applications . This article reviews the history, development and industrial applications of the PLC

A bilinear extension inequality in two dimensions

AbstractWe provide sharp decay estimates for circular averages of a certain bilinear extension operator on L2(S1)×L2(S1)

In vitro propagation of Eucalyptus species

Introduction The importance of eucalypts and reasons for tissue culture Eucalypts are Australia's most distinctive plant group. They are contained within the genus Eucalyptus which consists of over 500 named species, with more as yet unnamed (Brooker & Kleinig 1983; 1990 Chippendale 1988). The natural distribution of the genus is almost completely confined to the Australian continent and Tasmania with only two species, E. deglupta and E. urophylla, occurring naturally in other countries. Since European settlement of Australia, seeds of eucalypts have been sent to countries throughout the world and they are now commonly grown in tropical and temperate areas for timber, pulp wood, eucalyptus oil, fuelwood, charcoal and as ornamentals. Exploitation of eucalypts outside Australia was initiated by the French. During the nineteenth century, eucalypts were planted in Europe and North America, and European imperial governments introduced them to colonies in South America, Africa and Asia. The presence of eucalypts in some of these countries is now so familiar to the native peoples that many consider them to be indigenous (Zacharin 1978). Although eucalypts in early plantations often grew very quickly the wood was sometimes of poor quality due to wood splitting and distortion (Clarke 1957; Penfold & Willis 1961; Pryor 1976). In many cases this was because the species chosen were inappropriate for local climatic and edaphic conditions (Evans 1980; Durand-Cresswell et al. 1982), the trees had been planted for the wrong purposes (Penfold & Willis 1961; Pryor 1976), or given incorrect fertilisers (Savory 1962; Stone 1968). The poor quality of the wood led to a slump in enthusiasm for growing eucalypts until about 1945 when world demand for pulpwood started to increase (Pryor 1976). Today the major uses of eucalypt wood are for fuelwood and pulpwood. There has been a 150 fold increase in pulpwood production from eucalypts since the early 1960s (Molleda 1984). They are now the most widely planted hardwood group in the world (Boland et al. 1984; Eldridge et al. 1993)

A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

Assessing Urban Land Governance in Ethiopian Cities (2002-2011):Lessons for the 2011 Urban Land Management Policy Implementation

The people and lands of Ethiopia partake in the global movement towards urbanization. However, the land-to-people interfaces in urban Ethiopia are considered far from sustainable. This paper explores this assumption through the analytical lens of land governance and land administration. It considered the implementation of the urban land leasehold law from 2002-2011. Empirical data were collected from three case study cities in Ethiopia. A SWOT analysis technique with an additional priority component was employed. The SWOT analysis results indicated that the land administration and land governance situation in the case study cities during 2002-2011 were deterred by the lack of: an underlying land policy, independent responsible institution, coordination between different institutions, societal participation, and weak enforcement of laws and spatial plans. Priority areas that should improve these shortcomings and support future strategic planning and land development are identified. Overall, this study provides lessons for the implementation of the 2011 urban land policy to achieve its desired outcomes such as sustainable urban development

A note on bound entanglement and local realism

We show using a numerical approach that gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation.Comment: 5 page

Mixture of multiple copies of maximally entangled states is quasi-pure

Employing the general BXOR operation and local state discrimination, the mixed state of the form \rho^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|\phi_{mn}><\phi_{mn}|)^{\otim es k} is proved to be quasi-pure, where $\{|\phi_{mn}>\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d$. Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.Comment: 6 pages, 1 figure. The paper is subtantially revised and the general proof is give

Evaluation of UAV-based technology to capture land rights in Kenya: displaying stakeholder perspectives through interactive gaming

Limitations of western-oriented land administration systems and traditional surveying approaches have indisputably contributed to a reality where approximately 70% of the world’s land rights are not recorded. Amongst others, unmanned aerial vehicles (UAVs) are evolving as a remote sensing tool for alternative data acquisition. However, so far UAVs have only been tested and rarely been implemented in the context of land tenure mapping. To investigate technology uptake and to unlock the potential of UAV-based remote sensing, this paper introduces an interactive workshop approach. Key stakeholders are asked to rank four different means of data acquisition, namely satellite images, aerial images, UAV images, and ground surveying according to six predefined parameters. The results of the board game visually unveiled opportunities and drawbacks of each data acquisition technology from the perspective of the stakeholder while the group discussion provided valuable insights into existing workflows and different perceptions. Results reveal that on average, UAV-based images have the potential to compete with the currently most prevalent data collection technology - field surveying - as UAV-based images mostly ranked similar, except in terms of time efficiency (UAV images outperform field surveying) and accuracy (field surveying outperforms UAV images)