Notes on multiplicativity of maximal output purity for completely positive qubit maps

A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum value of the purity one can get at the output of a channel by varying over all physical input states, when purity is measured by the Schatten $q$-norm, and is denoted by $\nu_q$. The multiplicativity problem is the question whether two channels used in parallel have a combined $\nu_q$ that is the product of the $\nu_q$ of the two channels. A positive answer would imply a number of other additivity results in QIT. Very recently, P. Hayden has found counterexamples for every value of $q>1$. Nevertheless, these counterexamples require that the dimension of these channels increases with $1-q$ and therefore do not rule out multiplicativity for $q$ in intervals $[1,q_0)$ with $q_0$ depending on the channel dimension. I argue that this would be enough to prove additivity of entanglement of formation and of the classical capacity of quantum channels. More importantly, no counterexamples have as yet been found in the important special case where one of the channels is a qubit-channel, i.e. its input states are 2-dimensional. In this paper I focus attention to this qubit case and I rephrase the multiplicativity conjecture in the language of block matrices and prove the conjecture in a number of special cases.Comment: Manuscript for a talk presented at the SSPCM07 conference in Myczkowce, Poland, 10/09/2007. 12 page

Setting high expectations is not enough: linkages between expectation climate strength, trust, and employee performance

Drawing on Climate Theory and Social Exchange Theory, we examine whether and how the strength of the expectation climate, defined as the degree of agreement amongst job incumbents on what is expected from them, affects their job performance. To explain this relationship, we utilize mediating trust-in-the-organization effects as an explanatory avenue. In a time-lagged data sample of 568 public service employees, whose job performance is rated by their 242 line managers, we apply multilevel modelling. We employed stratified random sampling techniques across 75 job functions in a large, public sector organization in Belgium. Our analysis provides support for the argument that expectation climate strength via mediating trust-in-the-organization effects impacts positively on the relationship between employee expectations and performance. Specifically, the significant association of the expectation climate strength with trust suggests that the perceived consensus about the expectations among different job incumbents demonstrates an organization’s trustworthiness and reliability to pursue intentions that are deemed favorable for employees. We conjecture that expectation climate strength breeds trust which strengthens employees’ job performance. HRM professionals in general, and line managers in particular, should heed our advice and carefully manage their tools and practices in an effort to signal compatible expectancies to different job incumbents in the same or similar roles. Our results shed new light on the mechanisms through which the strength of collective expectations impacts employee outcomes

Combining High Yields and Blast Resistance in Rice (Oryza spp.): A Screening under Upland and Lowland Conditions in Benin

The future security of the supply of rice for food in Africa depends on improving the level of local production to achieve self-sufficiency. In order to cope with the existing gap between production and actual demand, combining a high level of rice blast tolerance and a high-yield potential is necessary. The current study was conducted under upland and lowland conditions in Benin to gain insight into the performance of selected blast-resistant accessions along with some currently grown varieties. This study revealed a high phenotypic variability among these accessions. Furthermore, differences in the performance of these accessions under lowland and upland conditions were observed. Principal component analysis showed their grouping in three clusters. The analysis also demonstrated a high yield potential among the blast-resistant rice accessions whether they were Oryza sativa or O. glaberrima. Furthermore, there was a significant correlation between yield and both spikelet fertility and growth cycle duration. In conclusion, the present study identified promising rice accessions for future breeding. High phenotypic variability in combination with interesting traits can help to develop new resilient varieties. Finally, when the traits correlate with yield, they can be used as markers for an early screening method for identifying promising accessions at an early stage

Binegativity and geometry of entangled states in two qubits

We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that the partial transposition can give another separable approximation of the entangled state in two qubits.Comment: 5 pages, 3 figures. I made the proof more transparen

Quantum benchmark for storage and transmission of coherent states

We consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this footing.Comment: 4 pages, references added, minor change

Leader-employee congruence of expected contributions in the employee-organization relationship

Employees' expected contributions can be incongruent with those of their leader. We examine the congruence effect of leaders' and employees' expected contributions on job satisfaction. Results of cross-level polynomial regressions on 947 employees and 224 leaders support the congruence effect. When expected contributions are congruent, employees are more satisfied with their job. Our findings suggest that employees enjoy high challenges, as long as these challenges are in harmony with the expected contributions of their leaders. Employees are less satisfied with their jobs both when their expected contributions were higher than their leaders' and when their expected contributions were lower than those of their leaders. Beyond the relevance of having high expected contributions, the findings highlight the crucial role played by the congruence of expected contributions of leaders and employees

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin

REACH implementation costs in the Belgian food industry:a semi-qualitative study

In this paper we discuss how companies in the Belgian food industry are affected by the REACH legislation and whether their competitiveness is weakened as a result. The study has been carried out through an extensive literature study, an electronic survey, in-depth interviews and a case-study. No indication is observed of REACH compliance significantly hampering the competitive position of Belgian food industry. The overall cost burden seems to be relatively low. In contrast with the chemical industry, large food companies bear the highest costs, whereas the financial impact on small and medium-sized food companies remains limited.<br

Mode-Wise Entanglement of Gaussian States

We address the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single mode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bi-partite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of "isotropic" states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.Comment: 4 pages, RevTex4. Replaced with revised version with reference added to a previous related paper. Minor typographical errors correcte