The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (see Shimony [1] and Barnum and Linden [2]), is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary twoqubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of threequbit GHZ, W and inverted-W states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.

Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy.

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Spin-triplet superfluids can support exotic objects, such as half-quantum vortices characterized by the nontrivial winding of the spin structure. We present cantilever magnetometry measurements performed on mesoscopic samples of Sr(2)RuO(4), a spin-triplet superconductor. With micrometer-sized annular-shaped samples, we observed transitions between integer fluxoid states as well as a regime characterized by "half-integer transitions"--steps in the magnetization with half the height of the ones we observed between integer fluxoid states. These half-height steps are consistent with the existence of half-quantum vortices in superconducting Sr(2)RuO(4).

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