We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure and the second is the $q$-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same $q$-squashed entanglement.

• Received 1 September 2007

DOI:https://doi.org/10.1103/PhysRevA.76.054303