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2007•Physical Review AOpen access

Bounds on the multipartite entanglement of superpositions

Wei Song, Nai-Le Liu, Zeng‐Bing Chen

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Quantum entanglement, Multipartite entanglement, Squashed entanglement, Multipartite, W state, Measure (data warehouse), Superposition principle, Quantum mechanics

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