I’ve had a few scholarly items come out in the past several weeks—new stuff, and updated versions of old stuff. Here are their coordinates:
Wikipedia has claimed for over 3 years now that John von Neumann was the ‘first quantum Bayesian’. In context, this reads as stating that von Neumann inaugurated QBism, the approach to quantum theory promoted by Fuchs, Mermin and Schack. This essay explores how such a claim is, historically speaking, unsupported.
“Sporadic SICs and the Normed Division Algebras.” arXiv:1605.01426 [quant-ph].
Recently, Zhu classified all the SIC-POVMs whose symmetry groups act doubly transitively. Lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups.
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.