Entanglement and coherence in quantum state merging

Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging where two parties aim to merge their parts of a tripartite quantum state. In standard quantum state merging, entanglement is considered as an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process, and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum, and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.Comment: 9 pages, 1 figure. Lemma 5 in Appendix D of the previous version was not correct. This did not affect the results of the main tex

Relevance of the observation of UHE gammas to hard X-ray astronomy

A number of consequences of the presence of sources of ultra high energy (UHE) gamma rays, exemplified by Cygnus X-3, are examined. It is shown that there should be a flux of hard X-rays at all Galactic latitudes; a significant flux of extragalactic hard X-rays may also result. Relevance to theories of cosmic ray particle origin and propagation is discussed

Fluctuation relations for heat engines in time-periodic steady states

A fluctuation relation for heat engines (FRHE) has been derived recently. In the beginning, the system is in contact with the cooler bath. The system is then coupled to the hotter bath and external parameters are changed cyclically, eventually bringing the system back to its initial state, once the coupling with the hot bath is switched off. In this work, we lift the condition of initial thermal equilibrium and derive a new fluctuation relation for the central system (heat engine) being in a time-periodic steady state (TPSS). Carnot's inequality for classical thermodynamics follows as a direct consequence of this fluctuation theorem even in TPSS. For the special cases of the absence of hot bath and no extraction of work, we obtain the integral fluctuation theorem for total entropy and the generalized exchange fluctuation theorem, respectively. Recently microsized heat engines have been realized experimentally in the TPSS. We numerically simulate the same model and verify our proposed theorems.Comment: 9 page

Modeling Bangladesh's gross domestic product using regression approach

This study finds the factors that affect Bangladesh’s Gross Domestic Product (GDP) through regression approach. Stepwise and Ridge regression techniques have been applied to build the suitable regression model. Model adequacy also has been checked and multicollinearity problem is addressed for a plausible model using appropriate remedial measures for each of the model one after another that yields stepwise regression. The multicollinearity problem has also been tried to combat by ridge regression. Finally, the model which is adequate and free from multicollinearity problem after applying the ridge regression has been considered as the credible model for predicting the GDP of Bangladesh. The final model shows that the factors population, imports of goods and services, agriculture value added, manufacturing value added and labor force are positively affecting the GDP of Bangladesh

Research Notes : Factor analysis in F2 generation of soybean crosses

Factor analysis is a technique of reducing a large number of correlated variables to a few main factors. It has been resorted to to overcome the limi-tations of univariate methods of analysis like correlations, path-coefficient and regression analysis (Wright, 1960; Walton, 1972). Besides, Moreno and Cubero (1978) have used it for estimating diversity

Effects of lubricated surface in the stagnation point flow of a micropolar fluid

In this investigation, we have considered a steady, two-dimensional flow of a micropolar fluid towards a stagnation point over a lubricated plate. A power law fluid is utilized for the purpose of lubrication. To derive the slip condition in the present flow situation, continuity of shear stress and velocity has been imposed at the fluid lubricant interface. The set of nonlinear coupled ordinary differential equations subject to boundary conditions is solved by a powerful numerical technique called the Keller-box method. Some important flow features have been analyzed and discussed under the influence of slip parameter , material parameter and ratio of micro-rotation to the skin friction parameter . The main purpose of the present article is to analyze the reduction in the shear stress and couple stress effects in the presence of lubrication as compared to the viscous fluid that may be beneficial during polymeric processing

Cosmic Needles versus Cosmic Microwave Background Radiation

It has been suggested by a number of authors that the 2.7K cosmic microwave background (CMB) radiation might have arisen from the radiation from Population III objects thermalized by conducting cosmic graphite/iron needle-shaped dust. Due to lack of an accurate solution to the absorption properties of exceedingly elongated grains, in existing literature which studies the CMB thermalizing process they are generally modelled as (1) needle-like spheroids in terms of the Rayleigh approximation; (2) infinite cylinders; and (3) the antenna theory. We show here that the Rayleigh approximation is not valid since the Rayleigh criterion is not satisfied for highly conducting needles. We also show that the available intergalactic iron dust, if modelled as infinite cylinders, is not sufficient to supply the required opacity at long wavelengths to obtain the observed isotropy and Planckian nature of the CMB. If appealing to the antenna theory, conducting iron needles with exceedingly large elongations (10^4) appear able to provide sufficient opacity to thermalize the CMB within the iron density limit. But the applicability of the antenna theory to exceedingly thin needles of nanometer/micrometer in thickness needs to be justified.Comment: 13 pages, 4 figures; submitted to ApJ