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Mathematics 2016, 4(2), 36;

SIC-POVMs and Compatibility among Quantum States

Physics Department, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston, MA 02125, USA
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Received: 1 March 2016 / Revised: 8 May 2016 / Accepted: 14 May 2016 / Published: 1 June 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
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An unexpected connection exists between compatibility criteria for quantum states and Symmetric Informationally Complete quantum measurements (SIC-POVMs). Beginning with Caves, Fuchs and Schack’s "Conditions for compatibility of quantum state assignments", I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting properties. Compatibility criteria provide a new way to understand the relationship between SIC-POVMs and mutually unbiased bases, as calculations in the SIC representation of quantum states make clear. This, in turn, illuminates the resources necessary for magic-state quantum computation, and why hidden-variable models fail to capture the vitality of quantum mechanics. View Full-Text
Keywords: SIC-POVM; qutrit; post-Peierls compatibility; Quantum Bayesian; QBism SIC-POVM; qutrit; post-Peierls compatibility; Quantum Bayesian; QBism

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Stacey, B.C. SIC-POVMs and Compatibility among Quantum States. Mathematics 2016, 4, 36.

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