Fig. 3: The comparison of \({n}_{\min }({{{{\mathcal{S}}}}}_{{\mathbb{I}}/{d}^{2}},\epsilon )\) and \({n}_{\min }({{{{\mathcal{S}}}}}_{{\zeta }_{i}},\epsilon )\). | Communications Physics

Fig. 3: The comparison of \({n}_{\min }({{{{\mathcal{S}}}}}_{{\mathbb{I}}/{d}^{2}},\epsilon )\) and \({n}_{\min }({{{{\mathcal{S}}}}}_{{\zeta }_{i}},\epsilon )\).

From: Teleportation with embezzling catalysts

Fig. 3

In (a), we sketch our idea and visualize the relation between the maximally mixed state \({\mathbb{I}}/{d}^{2}\) and the four random full-ranked states ζi with i ∈ {1, 2, 3, 4}. Each point of the line represents a possible τ considered in Eq. (24). In (b) to (e), the red and blue bar graphs respectively represent the number of copies of τ, with the red dotted line indicating the percentage of copy reduction, i.e., ϑ(ϵ), defined in Eq. (47).

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