What limits the success probability in LCU block encodings?

Question: In a Linear Combination of Unitaries construction, suppose A = Σ_j α_j U_j with positive coefficients α_j and normalization λ = Σ_j α_j. What is the subtle role of λ? A) It is only a bookkeeping constant and never affects success amplitude B) It is the eigenvalue gap of A used by phase estimation C) It sets the normalization of the block encoding, so larger λ can reduce raw postselection success and increase amplification cost D) It is the number of controlled unitary calls required regardless of precision Correct: C Explanation: LCU methods embed A/λ in a larger unitary. If the desired operation is obtained through postselection, the normalization influences the success amplitude. Amplitude amplification or related techniques may be needed to boost the success probability. Topic: advanced quantum computing / LCU / block encoding