Tight bounds on the concurrence of quantum superpositions

Abstract

The entanglement content of superpositions of quantum states is investigated based on a measure called {\it 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 in [Phys. Rev. Lett. 97, 100502 (2006).]

7 pages, 2 figures

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• Simple sufficient condition for subspace to be completely or genuinely entangled
• Separability and entanglement in superpositions of quantum states
• The Bound of Entanglement of Superpositions with More Than Two Components
• Quantifying subspace entanglement with geometric measures
• Character of superposed states under deterministic LOCC
• Local transformations of superpositions of entangled states
• Distribution of Standard deviation of an observable among superposed states
• To share and not share a singlet: control qubit and nonclassicality in teleportation
• Bounds on positive operator-valued measure based coherence of superposition
• Unconditionally superposition-robust entangled state in all multiparty quantum systems