Abstract
Entanglement Rényi-α entropy is an entanglement measure. It reduces to the standard entanglement of formation when α tends to 1. We derive analytical lower and upper bounds for the entanglement Rényi-α entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rényi-α entropy and some other entanglement measures.
Highlights
Quantum entanglement is one the most remarkable features of quantum mechanics and is the key resource central to much of quantum information applications
We establish the relation between entanglement Rényi-α entropy (ERαE) and other well-known entanglement measures, such as the entanglement of formation, the geometric measure of entanglement[52], the logarithmic negativity and the G-concurrence
Entanglement Rényi-α entropy is an important generalization of the entanglement of formation, and it reduces to the standard entanglement of formation when α approaches to 1
Summary
Quantum entanglement is one the most remarkable features of quantum mechanics and is the key resource central to much of quantum information applications. Chen et al.[18] derived an analytic lower bound of EOF for an arbitrary bipartite mixed state, which established a bridge between EOF and two strong separability criteria. Based on this idea, there are several improved lower and upper bounds for EOF presented in refs 33–36. There are other measures such as entanglement Rényi-α entropy (ERαE) which is the generalization of the entanglement of formation. Similar to the convex roof in (2), the ERαE of a bipartite mixed state ρAB is defined as
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