SICs and Algebraic Number Theory
arXiv:1701.05200 · doi:10.1007/s10701-017-0090-7
Abstract
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
15 pages, 1 figure, AMS Latex, talk at the conference "Quantum and Beyond", Vaxjo, Sweden, 2016
References in corpus (4)
Cited by in corpus (20)
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- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
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- Discrete Wigner Functions from Informationally Complete Quantum Measurements
- Dimension towers of SICs. I. Aligned SICs and embedded tight frames
- Born's rule as a quantum extension of Bayesian coherence
- What are the minimal conditions required to define a SIC POVM?
- Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
- Compounds of symmetric informationally complete measurements and their application in quantum key distribution
- Mutually unbiased frames
- Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
- SIC-POVMs from Stark units: Prime dimensions n^2+3
- Implementation of discrete positive operator valued measures on linear optical systems using cosine-sine decomposition
- SICs: Some explanations
- Maximal Magic for Two-qubit States
- Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
- Ray class groups and ray class fields for orders of number fields
- SICs and the Triangle Group