Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0807.2876

Stabilizer states and local realism

Matthew Elliott

Published Jul 17, 2008• 2 citations
arXivHTMLPDF

Abstract

The central focus of this work is to make progress towards understanding entanglement as a resource for computation by examining the quantum correlations that can be extracted from stabilizer states. As such, we focus on the stabilizer formalism, local realism, and the convergence of the two.
DOI
10.48550/arxiv.0807.2876

Related papers

Quantum hypergraph states: a review

Davide Poderini, Dagmar Bruß, Chiara Macchiavello

Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary and stochastic local operations with classical communication, the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation, and to their non-stabilizer character, quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.

Reports on Progress in Physics•Jun 1, 2026•0 citations

Quantum Hypergraph States: A Review

Davide Poderini, Dagmar Bruß, Chiara Macchiavello

Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary (LU) and stochastic local operations with classical communication (SLOCC), the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation (MBQC), and to their non-stabilizer character - quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.

quant-pharXiv:2603.10917•Mar 12, 2026•0 citations

Quantum entanglement distillation in the stabilizer formalism

Erik Hostens

•Oct 12, 2007•2 citations

QUANTUM ENTANGLEMENT DISTILLATION IN THE STABILIZER FORMALISM

Faculteit Ingenieurswetenschappen, Departement Elektrotechniek

•Jan 1, 2007•0 citations

Extractable Work from Correlations

Martí Perarnau-Llobet, Karen V. Hovhannisyan, Marcus Huber +3 more

Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory.In this work, we study how to use correlations among quantum systems to optimally store work.We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems.We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations.We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy.Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.

arXiv:1407.7765•Physical Review X•Oct 22, 2015•269 citations

Theoretical study of decoherence mechanisms and entanglement dynamics with specific application to materials like superconductors, magnets, etc., and quantum computation

Philip C. E. Stamp, Jeroen Wiemer

•Nov 1, 2000•0 citations
Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary and stochastic local operations with classical communication, the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation, and to their non-stabilizer character, quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.
Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary (LU) and stochastic local operations with classical communication (SLOCC), the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation (MBQC), and to their non-stabilizer character - quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.
Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory.In this work, we study how to use correlations among quantum systems to optimally store work.We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems.We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations.We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy.Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.