Could anyone elaborate on how these three concepts relate to each other? According to Charlie Bennett's original paper BDSW96, EPP is equivalent to QEC in the sense that both have the hashing bound as capacity. I was quite confused since the EPP and QEC in the paper are rather specific(they did a proof by construction)... as these two areas have evolved greatly over these two decades, does such equivalence still hold? Is there any recent proof?
Mark Wilde in his book presented a proof of the hashing bound Thm 24.6.2, the capacity of depolarizing channel, based on typical space and its properties. And it's saying there exists some QECC that achieves the bound, I'm wondering if such proof can be extended to EPP
