In this paper we investigate the module-theoretic properties of ⊥− and >-reachability modules in terms of inseparability relations for the DL SRIQ. We show that, although these modules are not depleting or self-contained, they share the robustness properties of syntactic locality modules and preserve all justifications for an entailment.

Considered as a multipartite quantum system, time-multiplexed nonlinear Schrödinger solitons after collision are rigorously proved to become quantum entangled in the sense that their quadrature components of suitably selected internal modes satisfy the inseparability criterion. Clear physical insights for the origin of entanglement are given, and the required homodyne local oscillator pulse sha...

An explicit formula is given for the quantity of entanglement in the output state of a beam splitter, given the squeezed vacuum states input in each mode. For the general Gaussian states input, the necessary and sufficient condition for the inseparability of the output state from a beam splitter is given.

We compare theoretically the tripartite entanglement available from the use of three concurrent χ(2) nonlinearities and three independent squeezed states mixed on beamsplitters, using an appropriate version of the van Loock– Furusawa inequalities. We also define three-mode generalizations of the Einstein–Podolsky–Rosen paradox which are an alternative for demonstrating the inseparability of the...

We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as particle number. argue that even separable may contain entanglement fixed charge sectors, long the state cannot be separated into charge-conserving components. As witness of symmetric we study number (NE), $\mathrm{\ensuremath{\Delta}}{S}_{m}$, defined entropy change due to subsystem's ...

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological To-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated ...