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International Journal of Quantum Information

ENTANGLEMENT OF SUPERPOSITION OF MULTI-STATES

Songsong Li, Yibin Huang

Published Jun 1, 2008• 58 citations
Publisher

Abstract

In this letter, we investigate the entanglement of superposition of multi-states. Three cases are considered when the states in the superposition are mutually biorthogonal, mutually orthogonal and nonorthogonal. The relations between the entanglement of superposition and the entanglements of the superposed states are explored.
DOI
10.1142/s0219749908003712

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Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are biorthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one ebit more than the average of the entanglement of the two states being superposed. However, for more general states, the situation is very different.
In this paper, we use the concurrence vector as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by III concurrence, so that our results can be compared to those given in Phys. Rev. A 76, 042328 (2007). We obtain a tighter lower bound in the case in which the two superposed states are orthogonal. We also show that when the two superposed states are not necessarily orthogonal, both lower and upper bounds are, in general, tighter than the bounds given in terms of the III concurrence. An extension of the results to the case with more than two states in the superpositions is also given.