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Keywords = post-Peierls compatibility

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14 pages, 337 KiB  
Article
SIC-POVMs and Compatibility among Quantum States
by Blake C. Stacey
Mathematics 2016, 4(2), 36; https://doi.org/10.3390/math4020036 - 1 Jun 2016
Cited by 19 | Viewed by 5890
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
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