21. Although less used, the separability assumption is considered more general because every stochastic process has a separable version. 22. The separability of " S " depends both on the Hamiltonian and on the choice of generalized coordinates. 23. In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian. 24. Thus every positive, but not completely positive, map ? gives rise to a necessary condition for separability in this way. 25. Extending the definition of separability from the pure case, we say that a mixed state is separable if it can be written as 26. This follows from the fact that for every normed space " Y ", separability of the continuous dual implies separability. 27. This follows from the fact that for every normed space " Y ", separability of the continuous dual implies separability . 28. A number of indicators of approximate separability can be used, see Golyandina et al . ( 2001, Ch . 1 ). 29. The two kinds of information have to be extracted on different occasions, because of the non-separability of the wave function representation. 30. For the and cases, a necessary and sufficient criterion for separability is given by the famous Positive Partial Transpose ( PPT ) condition.
