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Concurrence, Tangle and Fully Entangled Fraction of Quantum Entanglement

Ming Li, Shao-Ming Fei, Xianqing Li‐Jost, Zhi‐Xi Wang

Published Aug 17, 2009• 0 citations
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Abstract

We show that although we can not distill a singlet from many pairs of bound entangled states, the concurrence and tangle of two entangled quantum states are always strictly larger than that of one, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.

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The entanglement content of superpositions of quantum states is investigated based on a measure called concurrence. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we find simple inequalities relating the concurrence of the state to that of its components. We derive an exact expression for the concurrence when the component states are biorthogonal and provide elegant upper and lower bounds in all other cases. For quantum bits, our upper bound is tighter than the previously derived bound [N. Linden et al., Phys. Rev. Lett. 97, 100502 (2006)].