Year: 2020
Type: article
Abstract: The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state $\ensuremath{\rho}$ 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 $\mathcal{E}({\ensuremath{\rho}}^{\ensuremath{\bigotimes}N})$ is scalable if it can be described as a function of the variables ${\mathcal{E}({\ensuremath{\rho}}^{\ensuremath{\bigotimes}{i}_{1}}),\ensuremath{\cdots},\mathcal{E}({\ensuremath{\rho}}^{\ensuremath{\bigotimes}{i}_{q}});N}$ for $N>{i}_{j}$, while preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of $\mathcal{E}({\ensuremath{\rho}}^{\ensuremath{\bigotimes}N})$, which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if $\mathcal{E}({\ensuremath{\rho}}^{\ensuremath{\bigotimes}{2}^{n}})$ depends only on $\mathcal{E}(\ensuremath{\rho}), \mathcal{E}({\ensuremath{\rho}}^{\ensuremath{\bigotimes}2})$, and $n$, 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 $\ensuremath{\varrho}$, we determine the OSD entanglement for ${\ensuremath{\varrho}}^{\ensuremath{\bigotimes}96}$ from smaller tensorings, with an accuracy of $97%$ and no extra computational effort. Finally, we show that superactivation of nonadditivity may occur in this context.
Source: Physical Review A
Author: Fernando Parisio
Institution: Universidade Federal de Pernambuco
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G8423209235
OpenAlex ID: W3040784105