Quantum Sequential Hypothesis Testing

Esteban Martínez Vargas, Christoph Hirche, Gael Sentís, Michalis Skotiniotis, Marta Carrizo, Ramon Muñoz-Tapia, and John Calsamiglia
Phys. Rev. Lett. 126, 180502 – Published 6 May 2021
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Abstract

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular, our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold ε when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows us to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as log1/ε, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., ε=0.

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  • Received 23 November 2020
  • Accepted 13 April 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.180502

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Esteban Martínez Vargas1,*, Christoph Hirche2,†, Gael Sentís1,‡, Michalis Skotiniotis1,§, Marta Carrizo1, Ramon Muñoz-Tapia1,∥, and John Calsamiglia1,¶

  • 1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
  • 2QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark

  • *Esteban.Martinez@uab.cat
  • christoph.hirche@gmail.com
  • Gael.Sentis@uab.cat
  • §michail.skoteiniotis@uab.cat
  • Ramon.Munoz@uab.cat
  • John.Calsamiglia@uab.cat

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Issue

Vol. 126, Iss. 18 — 7 May 2021

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