SIC-POVMs and Compatibility among Quantum States

An unexpected connection exists between compatibility criteria for quantum states and symmetric informationally complete POVMs. Beginning with Caves, Fuchs and Schack's "Conditions for compatibility of quantum state assignments" [Phys. Rev. A 66 (2002), 062111], 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.Comment: 15 pages, 4 MUBs, 2 errata for CFS (2002), 1 graph with chromatic number 4. v4: journal versio

Masanes-Galley-M\"uller and the State-Update Postulate

Masanes, Galley and M\"uller claim to have derived a unique rule for quantum state update consequent upon a measurement outcome. Upon closer examination, their proof implicitly assumes its first step, namely that the state-update rule is linear.Comment: 3 page

A Critical, But Hopefully Cordial, QBist Reply to Ballentine

L. E. Ballentine's remarks in Physics Today about the QBist interpretation of quantum mechanics are generally wide of the mark.Comment: 6 pages nearly exactl