SIC-POVMs and Compatibility among Quantum States

Blake C. Stacey
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Blake C. Stacey: Physics Department, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston, MA 02125, USA

Mathematics, 2016, vol. 4, issue 2, 1-14

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.

Keywords: SIC-POVM; qutrit; post-Peierls compatibility; Quantum Bayesian; QBism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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