How quantum correlations enhance prediction of complementary measurements

If there are correlations between two qubits then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary \emph{knowledge excesses} are used. A non-trivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.Comment: 4 pages, 4 figure

Optical implementation of the encoding of two qubits to a single qutrit

We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore error-free any of the two encoded qubit states but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables to retrieve both qubits simultaneously with the average fidelity above 90% and we have proposed extension of the original encoding transformation to encode N qubits into one (N+1)-dimensional system.Comment: 6 pages, 3 figures, RevTeX

Inviscid incompressible limits of the full Navier-Stokes-Fourier system

We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on the three dimensional Euclidean space. The Euler-Boussinesq approximation is identified as the limit system

Multi-scale analysis of compressible viscous and rotating fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter \ep. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account

What kind of heat loss requirements NZEB and deep renovation sets for building envelope?

In most of countries the energy performance of buildings is defined as (primary) energy use of whole buildingâ s (heating, cooling, ventilation, DHW, lighting, HVAC auxiliary, appliances), not as specific requirements for building envelope. For construction companies of production of modular renovation panels it in necessary to know heat loss properties of building envelope (U, W/(m2â K); ï , W/(mâ K); ï £, W/K; q50, m3/(hâ m2)). In this study it is analyzed what kind of heat loss requirements exists for building envelope to meet on annual basis to following targets: nZEB i.e. national nearly zero energy definition; deep energy renovation with 80 % reduction of primary energy; ZEB i.e. net Zero Energy Building = the annual primary energy use = 0 kWh/(m² a). Indoor climate and energy calculations were made based on national energy calculation methodologies in six countries: Denmark, Estonia, Latvia, Czech Republic, Portugal, and Netherlands. Requirements for heat loss of building envelope vary depending on requirements on indoor climate and energy performance in specific country, outdoor climate, availability of renewable energy, and building typology. The thermal transmittance of the modular wall panels for nZEB was â 5% from pre renovation thermal transmittance in Latvia, â 10% in Estonia and up to 50% in Portugal. For roof the decrease of thermal transmittance was smaller mainly due to smaller thermal transmittance before renovation. Results show the difficulties to reach ZEB with multi-story apartment buildings in cold climate. There are not enough places to install renewables for energy production on site.The study has been conducted in the projects H2020 MoreConnect, TK146 the Estonian Centre of Excellence in Zero Energy and Resource Efficient Smart Buildings and Districts, ZEBE, IUT1−15 Nearly-zero energy solutions and their implementation on deep renovation of buildings

Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system

We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test functions. As a corollary we establish weak-strong uniqueness principle for the compressible Navier-Stokes system

Invasion biology in non-free-living species: interactions between abiotic (climatic) and biotic (host availability) factors in geographical space in crayfish commensals (Ostracoda, Entocytheridae)

In invasion processes, both abiotic and biotic factors are considered essential, but the latter are usually disregarded when modeling the potential spread of exotic species. In the framework of set theory, interactions between biotic (B), abiotic (A), and movement-related (M) factors in the geographical space can be hypothesized with BAM diagrams and tested using ecological niche models (ENMs) to estimate A and B areas. The main aim of our survey was to evaluate the interactions between abiotic (climatic) and biotic (host availability) factors in geographical space for exotic symbionts (i.e., non-free-living species), using ENM techniques combined with a BAM framework and using exotic Entocytheridae (Ostracoda) found in Europe as model organisms. We carried out an extensive survey to evaluate the distribution of entocytherids hosted by crayfish in Europe by checking 94 European localities and 12 crayfish species. Both exotic entocytherid species found, Ankylocythere sinuosa and Uncinocythere occidentalis, were widely distributed in W Europe living on the exotic crayfish species Procambarus clarkii and Pacifastacus leniusculus, respectively. No entocytherids were observed in the remaining crayfish species. The suitable area for A. sinuosa was mainly restricted by its own limitations to minimum temperatures in W and N Europe and precipitation seasonality in circum-Mediterranean areas. Uncinocythere occidentalis was mostly restricted by host availability in circum-Mediterranean regions due to limitations of P. leniusculus to higher precipitation seasonality and maximum temperatures. The combination of ENMs with set theory allows studying the invasive biology of symbionts and provides clues about biogeographic barriers due to abiotic or biotic factors limiting the expansion of the symbiont in different regions of the invasive range. The relative importance of abiotic and biotic factors on geographical space can then be assessed and applied in conservation plans. This approach can also be implemented in other systems where the target species is closely interacting with other taxa

Megaphylogeny resolves global patterns of mushroom evolution

peerReviewe

Weak-strong uniqueness property for the full Navier-Stokes-Fourier system

The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within the class of weak solutions