Simplest non-additive measures of quantum resources

• URL: http://arxiv.org/abs/2106.12651v2
• Date: Tue, 29 Jun 2021 13:17:33 GMT
• Title: Simplest non-additive measures of quantum resources
• Authors: L. F. Melo and Fernando Parisio
• Abstract summary: We study measures that can be described by $cal E(rhootimes N) =E(e;N) ne Ne$.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Given an arbitrary state $\rho$ and some figure of merit ${\cal E}(\rho)$, it is usually a hard problem to determine the value of ${\cal E}(\rho^{\otimes N})$. One noticeable exception is the case of additive measures, for which we simply have ${\cal E}(\rho^{\otimes N}) = Ne$, with $e\equiv {\cal E}(\rho)$. In this work we study measures that can be described by ${\cal E}(\rho^{\otimes N}) =E(e;N) \ne Ne$, that is, measures for which the amount of resources of $N$ copies is still determined by the single real variable $e$, but in a nonlinear way. If, in addition, the measures are analytic around $e=0$, recurrence relations can be found for the Maclaurin coefficients of $E$ for larger $N$. As an example, we show that the $\ell_1$-norm of coherence is a nontrivial case of such a behavior.

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