The SIC Question: History and State of Play
arXiv:1703.07901 · doi:10.3390/axioms6030021
Abstract
Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.
16 pages, 1 figure, many references; v3: updating bibliography, dimension eight hundred forty four
References in corpus (44)
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Tight informationally complete quantum measurements
- Introduction to the book "Quantum Theory: Informational Foundations and Foils"
- Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
- Constructing exact symmetric informationally complete measurements from numerical solutions
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- Experimental characterization of qutrits using SIC-POVMs
- Symmetric Informationally Complete Measurements of Arbitrary Rank
- Wigner tomography of two qubit states and quantum cryptography
- Introducing the Qplex: A Novel Arena for Quantum Theory
- Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices
- On SIC-POVMs in Prime Dimensions
- Quantification and manipulation of magic states
- SICs and Algebraic Number Theory
- Properties of the extended Clifford group with applications to SIC-POVMs and MUBs
- Fibonacci-Lucas SIC-POVMs
- SICs: Extending the list of solutions
- Self-testing properties of Gisin's elegant Bell inequality
- Experimental study of optimal measurements for quantum state tomography
- Optimal signal states for quantum detectors
- Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
- My Struggles with the Block Universe
- Mutually unbiased bases as minimal Clifford covariant 2-designs
- Maximally informative ensembles for SIC-POVMs in dimension 3
- Sequential measurements of conjugate observables
- On discrete structures in finite Hilbert spaces
- Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
- Accessible Information and Informational Power of Quantum 2-designs
- Magic informationally complete POVMs with permutations
- Tomographic and Lie algebraic significance of generalized symmetric informationally complete measurements
- Quantum Theory is a Quasi-stochastic Process Theory
- Quantum dynamical entropy, chaotic unitaries and complex Hadamard matrices
- State-independent contextuality with identical particles
- Representation of quantum states as points in a probability simplex associated to a SIC-POVM
- Galois Automorphisms of a Symmetric Measurement
- Quantum measurements with prescribed symmetry
- Phase-space representations of SIC-POVM fiducial states
- Associating vectors in $\CC^n$ with rank 2 projections in $\RR^{2n}$: with applications
- Sparse Signal Processing with Frame Theory
- MUBs and SIC-POVMs of a spin-1 system from the Majorana approach
- Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
- Single plane minimal tomography of double slit qubits
- Efficient and Robust Methods for Quantum Tomography
- Experimental realization of a single qubit SIC POVM on via a one-dimensional photonic quantum walk
Cited by in corpus (106)
- Constructing exact symmetric informationally complete measurements from numerical solutions
- Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms
- Characterizing nonclassical correlations via local quantum Fisher information
- The Numerics of Phase Retrieval
- Experimental single-setting quantum state tomography
- Enhanced entanglement criterion via symmetric informationally complete measurements
- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
- Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
- Optimal verification and fidelity estimation of maximally entangled states
- Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
- Hiding and masking quantum information in complex and real quantum mechanics
- QuanEstimation: An open-source toolkit for quantum parameter estimation
- Notwithstanding Bohr, the Reasons for QBism
- Probabilistic Simulation of Quantum Circuits with the Transformer
- Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
- Linking Entanglement Detection and State Tomography via Quantum 2-Designs
- Universally Fisher-Symmetric Informationally Complete Measurements
- Fibonacci-Lucas SIC-POVMs
- A family of multipartite separability criteria based on correlation tensor
- Entanglement detection with imprecise measurements
- Entropic uncertainty relations from equiangular tight frames and their applications
- Tight Frames, Hadamard Matrices and Zauner's Conjecture
- Resource-efficient high-dimensional entanglement detection via symmetric projections
- Semi-device-independent certification of independent quantum state and measurement devices
- Efficiency of photonic state tomography affected by fiber attenuation
- Probability representation of quantum dynamics using pseudostochastic maps
- Shadow tomography on general measurement frames
- Discrete Wigner Functions from Informationally Complete Quantum Measurements
- Dimension towers of SICs. I. Aligned SICs and embedded tight frames
- Implementation of generalized measurements on a qudit via quantum walks
- Born's rule as a quantum extension of Bayesian coherence
- Experimental demonstration of topological bounds in quantum metrology
- Implementation of quantum measurements using classical resources and only a single ancillary qubit
- What are the minimal conditions required to define a SIC POVM?
- Noncontextuality Inequalities from Antidistinguishability
- Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
- Lüders Channels and the Existence of Symmetric Informationally Complete Measurements
- Entanglement properties of multipartite informationally complete quantum measurements
- Five open problems in quantum information
- 9 4 = 6 6: Understanding the quantum solution to the Euler's problem of 36 officers
- Compounds of symmetric informationally complete measurements and their application in quantum key distribution
- Quantum Process Fidelity Bounds from Sets of Input States
- Optimal launch states for the measurement of principal modes in optical fibers
- Experimental quantum tomography assisted by multiply symmetric states in higher dimensions
- Approximate stabilizer rank and improved weak simulation of Clifford-dominated circuits for qudits
- Mutually unbiased frames
- Discrete and Continuous Welch Bounds for Banach Spaces with Applications
- Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis
- Entanglement criterion via general symmetric informationally complete measurements
- Simplified exact SICs
- Communication tasks in operational theories
- Bipartite quantum measurements with optimal single-sided distinguishability
- Enhancing quantum state tomography via resource-efficient attention-based neural networks
- Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
- Entanglement Breaking Rank and the existence of SIC POVMs
- Discrimination of POVMs with rank-one effects
- Quantum Measurements in the Light of Quantum State Estimation
- Minimal informationally complete measurements for probability representation of quantum dynamics
- Learning entanglement breakdown as a phase transition by confusion
- Hamiltonian tomography by the quantum quench protocol with random noise
- SIC-POVMs from Stark units: Prime dimensions n^2+3
- Quantum Theory as Symmetry Broken by Vitality
- SICs: Some explanations
- Entanglement criterion via general symmetric informationally complete measurement
- Uncertainty relations for quantum measurements from generalized equiangular tight frames
- On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
- Quantum measurements with prescribed symmetry
- Data-Driven Inference, Reconstruction, and Observational Completeness of Quantum Devices
- New Constructions and Characterizations of Flat and Almost Flat Grassmannian Fusion Frames
- Is the SIC Outcome There When Nobody Looks?
- Maximal Magic for Two-qubit States
- Aligned SICs and embedded tight frames in even dimensions
- Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
- Entanglement characterization by single-photon counting with random noise
- Quantum and Classical Bayesian Agents
- The Decompositions of Werner and Isotropic States
- Quantum State Tomography of Four-Level Systems with Noisy Measurements
- Optimal arrangements of classical and quantum states with limited purity
- Morphophoric POVMs, generalised qplexes, and 2-designs
- Moments of isotropic measures and optimal projective codes
- Repeated minimizers of -frame energies
- Misreading EPR: Variations on an Incorrect Theme
- Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
- Operational detection of entanglement via quantum designs
- Completeness Stability of Quantum Measurements
- Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
- Higher-dimensional symmetric informationally complete measurement via programmable photonic integrated optics
- Local measurement strategies for multipartite entanglement quantification
- Complementarity relations for design-structured POVMs in terms of generalized entropies of order
- Relating measurement disturbance, information and orthogonality
- SIC-POVMs from Stark Units: Dimensions n^2+3=4p, p prime
- Invariant Off-Diagonality: SICs as Equicoherent Quantum States
- Certifying the novelty of equichordal tight fusion frames
- Fibonacci Fervour in Linear Algebra and Quantum Information Theory
- A genetic algorithm to generate maximally orthogonal frames in complex space
- Geometric properties of SIC-POVM tensor square
- Operator Systems Generated by Projections
- p-adic Welch Bounds and p-adic Zauner Conjecture
- SICs and the Triangle Group
- Machine Learning of Quantum Entanglement from Noisy Measurements
- Dimension towers of SICs. II. Some constructions
- Generalized Numerical Construction of MUBs: A Group Theoretical Investigation
- Optical downlink modeling for low-earth-orbit and medium-earth-orbit satellites under atmospheric turbulence with a quantum-state-tomography use case
- Designing generalized elegant Bell inequalities in higher dimensions from a Tsirelson bound
- Quantum State Tomography of Photonic Qubits with Realistic Coherent Light Sources
- Enhanced separability criteria based on symmetric measurements