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We consider the simulation of a quantum channel by two parties who share a resource state and may apply local operations assisted by classical communication (LOCC).
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As a clarification on the literature, let us remark that the contribution of Ref. [ 13 ] is about this strong converse refinement. There is no “solidification” of the weak converse bounds and two-way capacities previously established by Ref. [ 12 ] , already fully computed in the first 2015 arXiv papers [ 35 , 36 ] . In these papers, the treatment of the shield system (which intervenes in definition of private state [ 37 ] ) is completely correct by an immediate application of a previous argument [ 38 , 39 ] which showed the exponential increase of the shield size for DV systems. This argument can be found in Eq. (21) of Ref. [ 35 , Version 2] for the case of DV channels. The extension to CV channels is achieved by just truncating the Hilbert space, as explicitly discussed afer Eq. (23) of Ref. [ 35 , Version 2] . The correctness of this approach has been also confirmed by later equivalent proofs present in the published version of the manuscript [ 12 ] , one of which does not even depend on the shield system. See Supplementary Note 3 of Ref. [ 12 ] for full details
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