bibkey: bodorkoniorczyk2017quantumroc
authors: András Bodor and Mátyás Koniorczyk
year: 2017
title: "Receiver Operation Characteristics of Quantum State Discrimination"
doi: 10.1007/s10946-017-9629-5
url: "https://arxiv.org/abs/1603.06801v1"
claim: "For two quantum states, binary discriminators give points (false-positive rate, true-positive rate) of a convex ROC domain whose upper boundary is the optimal ROC curve; the projective measurement of the Fuchs–Caves fidelity observable defines d+1 cumulative ROC points, and the paper leaves open whether these points lie on the optimal ROC curve."
strata_touched:
  - D5/S3/Quantum/Measurement/FidelityMeasurementROCRefutation
license: citation-only
triage: anchor

Bodor and Koniorczyk, Receiver operation characteristics of quantum state discrimination

A. Bodor and M. Koniorczyk, J. Russ. Laser Res. 38(2), 150–163 (2017); arXiv:1603.06801v1. Quotations are from the v1 TeX source.

The paper analyses the discrimination of two states ${\varrho }_N,{\varrho }_P$ through receiver operation characteristics: a discriminator gives the point $(\mathrm{FP},\mathrm{TP})$; the feasible ROC domain is convex, and the line of the best possible discriminators is the “optimal ROC curve”. A measurement whose outcomes are ordered by decreasing likelihood ratio gives cumulative points $(Q_k,P_k)$. In the proof that the quantum Bhattacharyya coefficient is at most the square-root fidelity, the paper uses the observable $$M={\varrho }_N^{-1/2}\sqrt{{\varrho }_N^{1/2}{\varrho }_P{\varrho }_N^{1/2}}{\varrho }_N^{-1/2}(44)$$ and states:

This obviously defines $d+1$ points in the feasible ROC domain, where $d$ stands for the dimension of the joint support of the two density operators. (It is an interesting open question whether these points are actually on the optimal ROC curve.)

Verified locator

Source: https://arxiv.org/abs/1603.06801v1

• DOI: https://doi.org/10.1007/s10946-017-9629-5 (Journal of Russian Laser Research 38(2), 150–163, 2017; title, authors, journal, volume, issue and pages from Crossref).
• URL: https://arxiv.org/abs/1603.06801v1. The e-print member Bodor_Koniorczyk_QuantumROC_submit_1.tex has 1121 lines and md5 2a4e9276a4036498640acd97004fb8f0. Locations:
  • the ROC domain, its convexity and the optimal ROC curve, l. 280–300;
  • cumulative points, l. 384–392;
  • the observable (44) and the open question, l. 934–944.