Fig. 5: The comparison of \({n}_{\min }({{{{\mathcal{S}}}}}_{{\mathbb{I}}/{d}^{2}},\epsilon )\) and \({n}_{\min }(100,\epsilon )\). | Communications Physics

Fig. 5: The comparison of \({n}_{\min }({{{{\mathcal{S}}}}}_{{\mathbb{I}}/{d}^{2}},\epsilon )\) and \({n}_{\min }(100,\epsilon )\).

From: Teleportation with embezzling catalysts

Fig. 5

a illustrates the required copies for enhancing average fidelity in entangled initial states. Left for 0.75, right for 0.80. The red and blue bar graphs illustrate the copies of τ (see Eq. (24)) corresponding to \({n}_{\min }({{{{\mathcal{S}}}}}_{{\mathbb{I}}/{d}^{2}},\epsilon )\) and \({n}_{\min }(100,\epsilon )\), respectively. b The case of separable initial states, improved to 0.7. Here, the red and blue bar graphs represent the average fidelity before and after embezzling. In both (a) and (b), the red dashed line indicates the percentage reduction in copies of \({n}_{\min }(100,\epsilon )\) compared to \({n}_{\min }({{{{\mathcal{S}}}}}_{{\mathbb{I}}/{d}^{2}},\epsilon )\). The random states selected by us are provided in Supplementary Tables 1 and 2.

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