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Mathematics 2016, 4(2), 36; doi:10.3390/math4020036

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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Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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

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