On polynomial invariants of several qubits

DOI10.1063/1.3075830zbMath1202.81017arXiv0804.1661OpenAlexW3098843617MaRDI QIDQ3650481

Andreas Osterloh, Dragomir Ž. Djoković

Publication date: 14 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1661

zbMATH Keywords

Hilbert spacespolynomialsinformation theoryquantum entanglementquantum computing

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Actions of groups on commutative rings; invariant theory (13A50) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (18)

Genuine multipartite entanglement measure ⋮ SLOCC classification of \(n\) qubits invoking the proportional relationships for spectrums and standard Jordan normal forms ⋮ Entanglement classification via integer partitions ⋮ Rank classification of tensors over ⋮ Polynomial measure of coherence ⋮ Cayley's hyperdeterminant: A combinatorial approach via representation theory ⋮ Entanglement of four-qubit systems: A geometric atlas with polynomial compass II (the tame world) ⋮ Geometry of the genus 9 Fano 4-folds ⋮ The invariant-comb approach and its relation to the balancedness of multipartite entangled states ⋮ On invariant notions of Segre varieties in binary projective spaces ⋮ Sequential generation of polynomial invariants and \(N\)-body non-local correlations ⋮ Quantum encoding and entanglement in terms of phase operators associated with harmonic oscillator ⋮ Entanglement of four qubit systems: A geometric atlas with polynomial compass I (the finite world) ⋮ CLASSIFICATION OF ENTANGLEMENT IN SYMMETRIC STATES ⋮ REE from EOF ⋮ Entanglement of four-qubit rank-2 mixed states ⋮ Erratum: “On polynomial invariants of several qubits” [J. Math. Phys. 50, 033509 (2009)] ⋮ ENTANGLEMENT AND ITS MULTIPARTITE EXTENSIONS

Cites Work

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• Geometry of three-qubit entanglement
• Multiparty entanglement in graph states
• Algebraic invariants of five qubits
• A complete set of covariants of the four qubit system
• Global entanglement in multiparticle systems
• On the geometry of four-qubit invariants
• ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS
• On the geometry of a class ofN-qubit entanglement monotones

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