Sequential Analysis of a finite number of Coherent states

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 $\sigma_0$ or $\sigma_1$ 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 $\{|\gamma\rangle,|-\gamma\rangle\}$ there is no advantage of taking any batch size $l$. We give an expression for the optimal batch size $l_\text{opt}$ in the assymetric case. We give bounds $l_\text{min}$ and $l_\text{max}$ for when $P_S\approx 1$.