Irreducible magic sets for n-Qubit systems

Magic sets of observables are minimal structures that capture quantum state-independent advantage for systems of n ≥ 2 qubits and are, therefore, fundamental tools for investigating the interface between classical and quantum physics. A theorem by Arkhipov (arXiv:1209.3819) states that n-qubit magic...

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Detalles Bibliográficos
Autores: Trandafir, Stefan, Lisoněk, Petr, Cabello Quintero, Adán
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/144738
Acceso en línea:https://hdl.handle.net/11441/144738
https://doi.org/10.1103/PhysRevLett.129.200401
Access Level:acceso abierto
Palabra clave:Magic sets
n-Qubit systems
Descripción
Sumario:Magic sets of observables are minimal structures that capture quantum state-independent advantage for systems of n ≥ 2 qubits and are, therefore, fundamental tools for investigating the interface between classical and quantum physics. A theorem by Arkhipov (arXiv:1209.3819) states that n-qubit magic sets in which each observable is in exactly two subsets of compatible observables can be reduced either to the twoqubit magic square or the three-qubit magic pentagram [N. D. Mermin, Phys. Rev. Lett. 65, 3373 (1990)]. An open question is whether there are magic sets that cannot be reduced to the square or the pentagram. If they exist, a second key question is whether they require n > 3 qubits, since, if this is the case, these magic sets would capture minimal state-independent quantum advantage that is specific for n-qubit systems with specific values of n. Here, we answer both questions affirmatively. We identify magic sets that cannot be reduced to the square or the pentagram and require n ¼ 3, 4, 5, or 6 qubits. In addition, we prove a generalized version of Arkhipov’s theorem providing an efficient algorithm for, given a hypergraph, deciding whether or not it can accommodate a magic set, and solve another open problem, namely, given a magic set, obtaining the tight bound of its associated noncontextuality inequality.