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We investigate the geometric characterization of pure state bipartiteentanglement of $(2\times{D})$- and $(3\times{D})$-dimensional compositequantum systems. To this aim, we analyze the relationship between states andtheir images under the action of particular classes of local unitaryoperations. We find that invariance of states under the action of single-qubitand single-qutrit transformations is a necessary and sufficient condition forseparability. We demonstrate that in the $(2\times{D})$-dimensional case thevon Neumann entropy of entanglement is a monotonic function of the minimumsquared Euclidean distance between states and their images over the set ofsingle qubit unitary transformations. Moreover, both in the $(2\times{D})$- andin the $(3\times{D})$-dimensional cases the minimum squared Euclidean distanceexactly coincides with the linear entropy (and thus as well with the tanglemeasure of entanglement in the $(2\times{D})$-dimensional case). These resultsprovide a geometric characterization of entanglement measures originallyestablished in informational frameworks. Consequences and applications of theformalism to quantum critical phenomena in spin systems are discussed.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Characterization of separability and entanglement in $(2\times{D})$- and  $(3\times{D})$-dimensional systems by single-qubit and single-qutrit unitary  transformations