Geometric and Information-Theoretic Properties of the Hoggar Lines
arXiv:1609.03075
Abstract
We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability distributions. Investigating the shape of this representation of state space yields a pattern of connections among a remarkable spread of mathematical constructions. In particular, studying the Shannon entropy of probabilistic representations of quantum states leads to an intriguing link between the questions of real and of complex equiangular lines. Furthermore, we will find relations between quantum information theory and mathematical topics like octonionic integers and the 28 bitangents to a quartic curve.
arXiv comment15 pages, 3 figures, 2 tables
References in corpus (16)
- Hidden Variables and the Two Theorems of John Bell
- Symmetric Informationally Complete Quantum Measurements
- Quantum-Bayesian Coherence: The No-Nonsense Version
- QBism, the Perimeter of Quantum Bayesianism
- Conditions for compatibility of quantum state assignments
- Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
- Quasiprobability representations of quantum mechanics with minimal negativity
- Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices
- Super-symmetric informationally complete measurements
- Quantum Conical Designs
- Informational power of the Hoggar SIC-POVM
- Exploring the geometry of qutrit state space using symmetric informationally complete probabilities
- SIC-POVMs and Compatibility among Quantum States
- Sporadic SICs and the Normed Division Algebras
- My Struggles with the Block Universe
- The many mathematical faces of Mermin's proof of the Kochen-Specker theorem
Cited by in corpus (11)
- Introducing the Qplex: A Novel Arena for Quantum Theory
- QBism: Quantum Theory as a Hero's Handbook
- Discrete Wigner Functions from Informationally Complete Quantum Measurements
- One-Shot Yield-Cost Relations in General Quantum Resource Theories
- Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
- The Penrose dodecahedron and the Witting polytope are identical in CP(3)
- Quantum Theory as Symmetry Broken by Vitality
- Is the SIC Outcome There When Nobody Looks?
- Misreading EPR: Variations on an Incorrect Theme
- Invariant Off-Diagonality: SICs as Equicoherent Quantum States
- QBism and the Ithaca Desiderata