2026-07-21T21:09:26Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20179 2024-07-02T07:52:50Z ddc:004 open_access

Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems Cautrès, Maxime Claudet, Nathan Mhalla, Mehdi Perdrix, Simon Savin, Valentin Thomassé, Stéphan Quantum networks graph states vertex-minors k-pairability We study the notion of k-stabilizer universal quantum state, that is, an n-qubit quantum state, such that it is possible to induce any stabilizer state on any k qubits, by using only local operations and classical communications. These states generalize the notion of k-pairable states introduced by Bravyi et al., and can be studied from a combinatorial perspective using graph states and k-vertex-minor universal graphs. First, we demonstrate the existence of k-stabilizer universal graph states that are optimal in size with n = Θ(k²) qubits. We also provide parameters for which a random graph state on Θ(k²) qubits is k-stabilizer universal with high probability. Our second contribution consists of two explicit constructions of k-stabilizer universal graph states on n = O(k⁴) qubits. Both rely upon the incidence graph of the projective plane over a finite field 𝔽_q. This provides a major improvement over the previously known explicit construction of k-pairable graph states with n = O(2^{3k}), bringing forth a new and potentially powerful family of multipartite quantum resources. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Maxime Cautrès and Nathan Claudet and Mehdi Mhalla and Simon Perdrix and Valentin Savin and Stéphan Thomassé 2024 Is Part Of LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2024.36 urn:nbn:de:0030-drops-201796 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.36 eng https://creativecommons.org/licenses/by/4.0/legalcode