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We examine two conditions that can be used to detect bipartite entanglement, and show that they can be used to provide lower bounds on the negativity of states. We begin with two-qubit states, and then show how what was done there can be extended to more general states. The resulting bounds are then studied by means of a number of examples. We also show that if one has some knowledge of the Schmidt vectors of a state, better bounds can be found.
Hillery et al. (Tue,) studied this question.