Robustness beyond the i.i.d. setting and under operational imperfections

Determine how the universal Schur–Weyl recovery mechanisms behave under imperfect operations and for sources or channels that depart from the independent-and-identically-distributed setting.

Background

The results are established primarily for tensor powers of a fixed bipartite state or memoryless quantum channel, with exact Schur–Weyl symmetry and ideal quantum operations. The authors explicitly identify robustness to implementation errors and non-i.i.d. structure as unresolved.

A solution would clarify whether the representation-theoretic coding mechanism continues to provide useful or optimal guarantees when the physical operations are noisy or when the copies exhibit correlations, nonstationarity, or other departures from the i.i.d. model.