Quantitative robustness bounds for measurement actions

Derive useful quantitative bounds for all measurement actions under the same local isometries used for the robust self-test of the reduced inner product game G5, thereby improving the qualitative convergence result that currently has no explicit measurement-error rate.

Background

The paper establishes an explicit robustness bound for state extraction from strategies for the five-dimensional reduced game G5, with error at most 2^21√ε for winning probability at least 1−ε. In contrast, the robustness theorem for the full strategy—including all 35 labeled measurement effects—provides only a dimension-independent modulus tending to zero as the winning probability approaches one, without an explicit rate.

The authors identify obtaining useful quantitative bounds for every measurement action under the same local isometries as an unresolved quantitative problem. Such bounds would strengthen the qualitative robustness result by specifying how measurement-action errors depend on the game-winning deficit ε.