Complexity of frustration: A new source of non-local non-stabilizerness
We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic", measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We...
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| Format: | Article |
| Language: | English |
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SciPost
2023-10-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.4.131 |
| _version_ | 1797666992932519936 |
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| author | Jovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, Salvatore Marco Giampaolo |
| author_facet | Jovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, Salvatore Marco Giampaolo |
| author_sort | Jovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, Salvatore Marco Giampaolo |
| collection | DOAJ |
| description | We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic", measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a $W$-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state's Stabilizer Rényi Entropy is the sum of that of the $W$-states plus an extensive local contribution. Our work reveals that $W$-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems. |
| first_indexed | 2024-03-11T20:06:43Z |
| format | Article |
| id | doaj.art-a4d3ac9d7b824090b234aad59a4342bb |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-11T20:06:43Z |
| publishDate | 2023-10-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-a4d3ac9d7b824090b234aad59a4342bb2023-10-03T14:43:02ZengSciPostSciPost Physics2542-46532023-10-0115413110.21468/SciPostPhys.15.4.131Complexity of frustration: A new source of non-local non-stabilizernessJovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, Salvatore Marco GiampaoloWe advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic", measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a $W$-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state's Stabilizer Rényi Entropy is the sum of that of the $W$-states plus an extensive local contribution. Our work reveals that $W$-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.https://scipost.org/SciPostPhys.15.4.131 |
| spellingShingle | Jovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, Salvatore Marco Giampaolo Complexity of frustration: A new source of non-local non-stabilizerness SciPost Physics |
| title | Complexity of frustration: A new source of non-local non-stabilizerness |
| title_full | Complexity of frustration: A new source of non-local non-stabilizerness |
| title_fullStr | Complexity of frustration: A new source of non-local non-stabilizerness |
| title_full_unstemmed | Complexity of frustration: A new source of non-local non-stabilizerness |
| title_short | Complexity of frustration: A new source of non-local non-stabilizerness |
| title_sort | complexity of frustration a new source of non local non stabilizerness |
| url | https://scipost.org/SciPostPhys.15.4.131 |
| work_keys_str_mv | AT jovanodavictobiashauggianpaolotorrealiosciahammafabiofranchinisalvatoremarcogiampaolo complexityoffrustrationanewsourceofnonlocalnonstabilizerness |