2026-09-18T21:13:59Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1398682022-02-08T03:02:45Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Oppenheim, Alan V.
Medlock, Catherine Aiko
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2022-02-07T15:09:36Z
2022-02-07T15:09:36Z
2021-09
2021-09-21T19:30:46.534Z
https://hdl.handle.net/1721.1/139868
The central topics of this thesis are operating characteristics for binary hypothesis testing in classical and quantum settings and overcomplete quantum measurements for quantum binary state discrimination. With this we explore decision and measurement operating characteristics defined as the tradeoff between probability of detection and probability of false alarm as parameters are varied. The thesis specifically addresses the Neyman-Pearson optimality of receiver operating characteristics when they are generated using threshold tests on the score variable rather than threshold tests on the likelihood ratio. The analysis applies to any scalar score variable. In the quantum setting, informationally overcomplete POVMs are explored to provide more robust quantum binary state discrimination schemes. We focus on equal trace rank one or Etro POVMs, which can be specified by arrangements of points on a sphere that we refer to as an Etro sphere.
Ph.D.
Sc.D.
Massachusetts Institute of Technology
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http://rightsstatements.org/page/InC-EDU/1.0/
Quantum State Discrimination with Overcompleteness
Thesis
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Doctoral
Doctor of Philosophy
Doctor of Science
Publication
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<Abstract>The central topics of this thesis are operating characteristics for binary hypothesis testing in classical and quantum settings and overcomplete quantum measurements for quantum binary state discrimination. With this we explore decision and measurement operating characteristics defined as the tradeoff between probability of detection and probability of false alarm as parameters are varied. The thesis specifically addresses the Neyman-Pearson optimality of receiver operating characteristics when they are generated using threshold tests on the score variable rather than threshold tests on the likelihood ratio. The analysis applies to any scalar score variable. In the quantum setting, informationally overcomplete POVMs are explored to provide more robust quantum binary state discrimination schemes. We focus on equal trace rank one or Etro POVMs, which can be specified by arrangements of points on a sphere that we refer to as an Etro sphere.</Abstract>
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