Abstract
We investigate an advantage for information processing of ordering a set of states over making a global quantum processing with a fixed number of copies of coherent states. Suppose Alice has N copies of one of two quantum states σ₀ or σ₁ and she gives these states to Bob. Using the optimal sequential test, the SPRT, we ask if processing the states in batches of size l is advantageous to optimally distinguish the two hypotheses. We find that for the symmetric case {|γ,|-γ} there is no advantage of taking any batch size l. We give an expression for the optimal batch size lopt in the assymetric case. We give bounds lmin and lmax for when P_S≈ 1.