Sequential Analysis of a finite number of Coherent states

TL;DR

This paper analyzes the benefits of sequentially processing a finite number of coherent quantum states for hypothesis testing, comparing batch processing to global processing, and provides optimal batch size bounds.

Contribution

It introduces a framework for evaluating sequential versus global processing of coherent states and derives optimal batch size expressions and bounds for high success probability.

Findings

No advantage for batch processing in symmetric case

Expression for optimal batch size in asymmetric case

Bounds for batch size when success probability approaches one

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 $\sigma_0$ 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 $P_S\approx 1$.