On the Geometric Measures of Entanglement

Abstract

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three qubit case is discussed and argued that the distance to the W states is a new monotone.

7 pages, 1 figures, minor content change, references added, 1 figure added

References in corpus (3)

• Hierarchies of Geometric Entanglement
• Universal geometric entanglement close to quantum phase transitions
• Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2

Cited by in corpus (7)

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• Optimal reducibility of all Stochastic Local Operation and Classical Communication equivalent W states
• Geometric analysis of entangled qubit pairs
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations