Article
Irreducible magic sets for n-Qubit systems
Author/s | Trandafir, Stefan
Lisoněk, Petr Cabello Quintero, Adán |
Department | Universidad de Sevilla. Departamento de Física Aplicada II |
Publication Date | 2022-11-07 |
Deposit Date | 2023-04-21 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Natural Sciences and Engineering Research Council of Canada (NSERC) Universidad de Sevilla European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Economia, Industria y Competitividad (MINECO). España Ministerio de Ciencia, Innovación y Universidades (MICINN). España |
Project ID. | RGPIN-2015-06250
RGPIN-2022-04526 US-15097 PCI2019-111885-2 PID2020–113738 GB-I00 |
Citation | Trandafir, S., Lisoněk, P. y Cabello Quintero, A. (2022). Irreducible magic sets for n-Qubit systems. Physical Review Letters, 129 (200401). https://doi.org/10.1103/PhysRevLett.129.200401. |
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