Abstract
The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we propose a way to circumvent the direct evaluation of such quantities, provided that the employed measures satisfy a self-similarity property. We say that a quantity is scalable if it can be described as a function of the variables for , while preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of , which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if depends only on , and , then it is completely determined by Fibonacci polynomials, to leading order. We show that the one-shot distillable (OSD) entanglement is well described as a scalable measure for several families of states. For a particular two-qutrit state , we determine the OSD entanglement for from smaller tensorings, with an accuracy of and no extra computational effort. Finally, we show that superactivation of nonadditivity may occur in this context.
- Received 22 October 2019
- Accepted 23 June 2020
DOI:https://doi.org/10.1103/PhysRevA.102.012413
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