Research proof index

If $(X_i)_{1 \leq i \leq m}$ is a $\tau$-minimizer, then $\sum_{i=1}^m d[X_i; X^0] \leq \frac{2m}{\eta} d[X^0; X^0]$.

Operator extension of SSA (Main result of Lin-Kim-Hsieh). For positive definite ρ_AB and σ_BC: ρ_A⁻¹ ⊗ σ_BC ≤ ρ_AB⁻¹ ⊗ σ_C where ρ_A = Tr_B(ρ_AB) and σ_C = Tr_B(σ_BC), and the RHS is reindexed via the associator (dA × dB) × dC ≃ dA × (dB × dC).

There exists an optimal T for the hypothesis testing, that is, it's a minimum and not just an infimum. This tightens the T from exists_min' to a ⟪ρ,T⟫ = 1 - ε bound.

There exists an optimal T for the hypothesis testing, that is, it's a minimum and not just an infimum. This states we have 1 - ε ≤ ρ.exp_val T, but we can always "worsen" T to make that bound tight, which is exists_min.

The space of strategies T in OptimalHypothesisRate is compact.

The space of strategies T in OptimalHypothesisRate is convex.