Quantum State Detector Design: Optimal Worst-Case a posteriori Performance

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dc.creatorKosut, Robert L.
dc.creatorWalmsley, Ian
dc.creatorEldar, Yonina
dc.creatorRabitz, Herschel
dc.date2004-03-21
dc.date.accessioned2026-07-07T06:09:20Z
dc.date.available2026-07-07T06:09:20Z
dc.descriptionThe problem addressed is to design a detector which is maximally sensitive to specific quantum states. Here we concentrate on quantum state detection using the worst-case a posteriori probability of detection as the design criterion. This objective is equivalent to asking the question: if the detector declares that a specific state is present, what is the probability of that state actually being present? We show that maximizing this worst-case probability (maximizing the smallest possible value of this probability) is a quasiconvex optimization over the matrices of the POVM (positive operator valued measure) which characterize the measurement apparatus. We also show that with a given POVM, the optimization is quasiconvex in the matrix which characterizes the Kraus operator sum representation (OSR) in a fixed basis. We use Lagrange Duality Theory to establish the optimality conditions for both deterministic and randomized detection. We also examine the special case of detecting a single pure state. Numerical aspects of using convex optimization for quantum state detection are also discussed.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0403150
dc.identifierhttp://arxiv.org/abs/quant-ph/0403150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91927
dc.subjectQuantum Physics
dc.titleQuantum State Detector Design: Optimal Worst-Case a posteriori Performance
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