286 citations · 1.1k across the 43 of their papers we have counts for
43 papers
SIC-POVMs from Stark units: Prime dimensions n^2+3
Marcus Appleby, Ingemar Bengtsson, Markus Grassl +2
We propose a recipe for constructing a SIC fiducial vector in complex Hilbert space of dimension of the form , focussing on prime dimensions . Such structures are sho…
Tight Frames, Hadamard Matrices and Zauner's Conjecture
Marcus Appleby, Ingemar Bengtsson, Steven Flammia +1
We show that naturally associated to a SIC (symmetric informationally complete positive operator valued measure or SIC-POVM) in dimension d there are a number of higher dimensional…
Simplified exact SICs
Marcus Appleby, Ingemar Bengtsson
In the standard basis exact expressions for the components of SIC vectors (belonging to a symmetric informationally complete POVM) are typically very complicated. We show that a si…
Dimension towers of SICs. I. Aligned SICs and embedded tight frames
Marcus Appleby, Ingemar Bengtsson, Irina Dumitru +1
Algebraic number theory relates SIC-POVMs in dimension to those in dimension . We define a SIC in dimension to be aligned to a SIC in dimension if and on…
Constructing exact symmetric informationally complete measurements from numerical solutions
Marcus Appleby, Tuan-Yow Chien, Steven Flammia +1
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. The…
Introducing the Qplex: A Novel Arena for Quantum Theory
Marcus Appleby, Christopher A. Fuchs, Blake C. Stacey +1
We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of modern quantum information theory, an…