Sequential Analysis of a finite number of Coherent states

• Published in: arXiv.org
• Main Author: Martínez-Vargas, Esteban
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.12.2022
• Subjects: Hypotheses; Optimization; Physics - Quantum Physics; Qubits (quantum computing); Sequential analysis
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2206.04604

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 \(P_S\approx 1\).