Purification and correlated measurements of bipartite mixed states

We prove that all purifications of a non-factorable state (i.e., the state which cannot be expressed in a form $\rho_{AB}=\rho_A\otimes\rho_B$) are entangled. We also show that for any bipartite state there exists a pair of measurements which are correlated on this state if and only if the state is non-factorable.Comment: 4 revtex pages, to appear in Phys. Rev.

Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis

The Relativistic Quantum Motions

Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we plot the relativistic quantum trajectories of a particle moving under the constant and the linear potentials. We establish the existence of nodes and link them to the de Broglie's wavelength.Comment: Latex, 18 pages, 3 eps figure

Optimality of private quantum channels

We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel $\cal E$ and von Neumann entropy of the ciphertext state $\varrho^{(0)}$. Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if exists) is optimizing the entropy. For non-ancillary single qubit PQC we have derived the optimal entropy for arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analyzed all the possible single qubit private quantum channels for arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.Comment: no commen

Fair and optimistic quantum contract signing

We present a fair and optimistic quantum contract signing protocol between two clients that requires no communication with the third trusted party during the exchange phase. We discuss its fairness and show that it is possible to design such a protocol for which the probability of a dishonest client to cheat becomes negligible, and scales as N^{-1/2}, where N is the number of messages exchanged between the clients. Our protocol is not based on the exchange of signed messages: its fairness is based on the laws of quantum mechanics. Thus, it is abuse-free, and the clients do not have to generate new keys for each message during the Exchange phase. We discuss a real-life scenario when the measurement errors and qubit state corruption due to noisy channels occur and argue that for real, good enough measurement apparatus and transmission channels, our protocol would still be fair. Our protocol could be implemented by today's technology, as it requires in essence the same type of apparatus as the one needed for BB84 cryptographic protocol. Finally, we briefly discuss two alternative versions of the protocol, one that uses only two states (based on B92 protocol) and the other that uses entangled pairs, and show that it is possible to generalize our protocol to an arbitrary number of clients.Comment: 11 pages, 2 figure

EVALUATING EXTENSIVE SHEEP FARMING SYSTEMS

Data from each of 5 commercial, extensive sheep farms in Cumbria, UK were used as parameters in a linear program (LP) representing labour and grazing management in such farming systems. The LP maximised ewe enterprise gross margin subject to constraints dictated by the labour availability and land types on each farm. Under the assumptions used, labour availability and price restricted ewe numbers well below those observed in practice on 2 farms i.e. land resources were adequate for the farming system practiced. On two other farms stocking levels and hence returns were limited by the availability of forage and hence feed input prices relative to output. On one farm, greater grassland productivity was the key determinant of system performance. It was concluded that a holistic systems approach was needed to properly evaluate these farming systems in terms of their potential contribution to animal welfare, land use, profit and hence their sustainabilityLivestock Production/Industries, Extensive, Sheep, Economics, LP,

Using quantum key distribution for cryptographic purposes: a survey

The appealing feature of quantum key distribution (QKD), from a cryptographic viewpoint, is the ability to prove the information-theoretic security (ITS) of the established keys. As a key establishment primitive, QKD however does not provide a standalone security service in its own: the secret keys established by QKD are in general then used by a subsequent cryptographic applications for which the requirements, the context of use and the security properties can vary. It is therefore important, in the perspective of integrating QKD in security infrastructures, to analyze how QKD can be combined with other cryptographic primitives. The purpose of this survey article, which is mostly centered on European research results, is to contribute to such an analysis. We first review and compare the properties of the existing key establishment techniques, QKD being one of them. We then study more specifically two generic scenarios related to the practical use of QKD in cryptographic infrastructures: 1) using QKD as a key renewal technique for a symmetric cipher over a point-to-point link; 2) using QKD in a network containing many users with the objective of offering any-to-any key establishment service. We discuss the constraints as well as the potential interest of using QKD in these contexts. We finally give an overview of challenges relative to the development of QKD technology that also constitute potential avenues for cryptographic research.Comment: Revised version of the SECOQC White Paper. Published in the special issue on QKD of TCS, Theoretical Computer Science (2014), pp. 62-8

Impacts of labour on interactions between economics and animal welfare in extensive sheep farms

This study quantified interactions between animal welfare and farm profitability in British extensive sheep farming systems. Qualitative welfare assessment methodology was used to assess welfare from the animal's perspective in 20 commercial extensive sheep farms and to estimate labour demand for welfare, based on the assessed welfare scores using data collected from farm inventories. The estimated labour demand was then used as a coefficient in a linear program based model to establish the gross margin maximising farm management strategy for given farm situations, subject to constraints that reflected current resource limitations including labour supply. Regression analysis showed a significant relationship between the qualitative welfare assessment scores and labour supply on the inventoried farms but there was no significant relationship between current gross margin and assessed welfare scores. However, to meet the labour demand of the best welfare score, a reduction in flock size and in the average maximum farm gross margin was often required. These findings supported the hypothesis that trade-offs between animal welfare and farm profitability are necessary in providing maximum animal welfare via on-farm labour and sustainable British extensive sheep farming systems.Sheep, Labour, Animal Welfare, Linear Programme, Livestock Production/Industries, C6, Q10, Q19, Q57,

A framework for estimating society’s economic welfare following the introduction of an animal disease: the case of Johne’s disease

Animal diseases are global issues affecting the productivity and financial profitability of affected farms. Johne’s disease is distributed on farms worldwide and is an endemic contagious bacterial infection in ruminants caused by Mycobacterium avium subspecies paratuberculosis. In cattle, the clinical disease manifests itself as chronic enteritis resulting in reduced production, weight loss, and eventually death. Johne’s disease is prevalent in the UK, including Scotland. Direct costs and losses associated with Johne’s disease have been estimated in previous research, confirming an important economic impact of the disease in UK herds. Despite this, the distributional impact of Johne’s disease among milk consumers and producers in Scotland has not been estimated. In this paper, we evaluate the change in society’s economic welfare, namely to dairy producers (i.e. infected and uninfected herds) and milk consumers in Scotland induced by the introduction of Johne’s disease in the national Scottish dairy herd. At the national-level, we conclude that the economic burden falls mainly on producers of infected herds and, to a lesser extent, milk consumers, while producers of uninfected herds benefit from the presence of Johne’s. An infected producer’s loss per cow is approximately two times larger in magnitude than that of an uninfected producer’s gain. Such economic welfare estimates are an important comparison of the relative costs of national herd prevalence and the wider economic welfare implications for both producers and consumers. This is particularly important from a policy, public good, cost sharing, and human health perspective. The economic welfare framework presented in this paper can be applied to other diseases to examine the relative burden of society’s economic welfare of alternative livestock disease scenarios. In addition, the sensitivity analysis evaluates uncertainty in economic welfare given limited data and uncertainty in the national herd prevalence, and other input parameters, associated with Johne’s disease in Scotland. Therefore, until the prevalence of Johne’s is better understood, the full economic cost to Scottish dairy herds remains uncertain but in the meantime the sensitivity analysis evaluates the robustness of economic welfare to such uncertainties