We classify the entanglement of two-mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This characterization allows for an experimentally reliable estimate of continuous variable entanglement based on measurements of purity.

Let κ = Fq be a finite field of characteristic p > 0, and k be a fixed algebraic closure of κ. We fix a prime ` 6= p, and an isomorphism τ : Q` → C. Whenever we want to denote something (e.g. scheme, sheaf, morphism, etc.) defined over κ, we will put a subscript 0 (e.g. X0 is a scheme over κ, F0 is a Weil sheaf defined over X0, etc.), and when the subscript is dropped, this means the correspond...

Three recrystallization technics were used to fractionate five commercial cholesterol products and one artificial mixture. One technic involved the recrystallization of cholesterol from absolute ethyl alcohol, the second technic involved the recrystallization of cholesterol from glacial acetic acid, and the third technic used the dibromide derivative method. The molar absorptivities for the var...

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. Thus, quantum me...

In the last 15 years NMR has become a reference technique for the determination of purity for organic standards containing NMR active nuclei [1, 2]. The puzzle proposed for this Analytical Challenge was focused on the use of 1H-NMR for the characterization of a phenylbutazone standard. Such material was purchased from Sigma-Aldrich and analyzed in parallel by HPLC-UV and 1H-NMR. Initially, appl...

Purity Analysis is the problem of determining whether or not a method may have side-effects. This has applications in automatic parallelisation, extended static checking, and more. We present a novel purity system for Java that employs purity annotations which can be checked modularly. This is done using a flow-sensitive, intraprocedural analysis. The system exploits two properties, called fres...

Many people judge suicide to be immoral. We have found evidence that these moral judgments are primarily predicted by people's belief that suicide taints the soul and by independent concerns about purity. This finding is inconsistent with accounts that define morality as fundamentally based upon harm considerations. In this commentary, we respond to a critique of our finding, and we provide fur...

We show that entanglement can always arise in the interaction of an arbitrarily large system in any mixed state with a single qubit in a pure state. This small initial purity is enough to enforce entanglement even when the total entropy is close to maximum. We demonstrate this feature using the Jaynes-Cummings interaction of a two-level atom in a pure state with a field in a thermal state at an...