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Physical Review A

Probability interpretation, an equivalence relation, and a lower bound on the convex-roof extension of negativity

Abbass Sabour, Mojtaba Jafarpour

Published Apr 24, 2012• 5 citations
Publisher

Abstract

We present a measure of entanglement for pure two-qutrit states which constitutes a probability interpretation for negativity. We also obtain an equivalence relation for the latter, which is used to find a lower bound on its convex-roof extension, for systems with dimensions up to 6. The possibility of the obtained results being valid for higher-dimensional systems is also discussed.

DOI
10.1103/physreva.85.042323

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We present a measure of entanglement for pure two-qutrit states which constitutes a probability interpretation for negativity. We also obtain an equivalence relation for the latter, which is used to find a lower bound on its convex-roof extension, for systems with dimensions up to 6. The possibility of the obtained results being valid for higher-dimensional systems is also discussed.
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We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and GGG concurrence. The lower bounds facilitate estimates of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures.