Operating Characteristics for Binary Hypothesis Testing in Quantum Systems
Name
operating_characteristics_bht_quantum_systems1.pdf
Description
Accepted version
Size
629.5 KB
Format
Adobe PDF
Checksum (MD5)
babc7d7d2a56e00445323a189ced5280
Author(s)
Medlock, Catherine(Catherine Aiko)
Oppenheim, Alan V.
Chuang, Isaac L.
Ding, Qi
Date Issued
September 2019
Journal
2019 57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Medlock, Catherine et al. “Operating Characteristics for Binary Hypothesis Testing in Quantum Systems.” Paper presented at the 2019 57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019, Monticello, IL, 24-27 Sept. 2019, IEEE © 2019 The Author(s)
Version
Author's final manuscript
Abstract
Receiver operating characteristics (ROCs) are a well-established representation of the tradeoff between detection and false alarm probabilities in classical binary hypothesis testing. We use classical ROCs as motivation for two types of operating characteristics for binary hypothesis testing in quantum systems - decision operating characteristics (QDOCs) and measurement operating characteristics (QMOCs). Both are described in the context of a framework we propose that encompasses the typical formulations of binary hypothesis testing in both the classical and quantum scenarios. We interpret Helstrom's well-known result [1] regarding discrimination between two quantum density operators with minimum probability of error in this framework. We also present a generalization of previous results [2], [3] regarding the correspondence between classical Parseval frames and quantum measurements. The derivation naturally leads to a constructive procedure for generating many different measurements besides Helstrom's optimal measurement, some standard and others non-standard, that achieve minimum probability of error.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/ALLERTON.2019.8919700
