It is usually believed that coarse-graining of quantum correlations leads to classical in the macroscopic limit. Such a principle, known as locality, has been proved for arising from independent and identically distributed (IID) entangled pairs. In this letter we consider generic (non-IID) scenario. We find Hilbert space structure theory can be preserved This directly Bell violation coarse-grai...

Abstract We prove that analogues of the Hardy–Littlewood generalised twin prime conjecture for almost primes hold on average. Our main theorem establishes an asymptotic formula number integers $n=p_1p_2 \leq X$ such $n+h$ is a product exactly two which holds all $|h|\leq H$ with $\log^{19+\varepsilon}X\leq H\leq X^{1-\varepsilon}$ , under restriction size one factors n and . Additionally, we co...

the quality of wastewater generated in any process industry is generally indicated by performance itrace metals in the aquatic environment have to date come essentially from naturally occurring geochemical resources. however, this has been enhanced by anthropogenic activities resulting in pollution. consequently, correlations and partitioning of trace metals in the dissolved phase, suspended pa...