Extremal Magic States from Symmetric Lattices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918057885040640 |
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| author | Ohta, Misaki Sakurai, Kazuki |
| author_facet | Ohta, Misaki Sakurai, Kazuki |
| contents | Magic, a key quantum resource beyond entanglement, remains poorly understood in terms of its structure and classification. In this paper, we demonstrate a striking connection between high-dimensional symmetric lattices and quantum magic states. By mapping vectors from the $E_8$, $BW_{16}$, and $E_6$ lattices into Hilbert space, we construct and classify stabiliser and maximal magic states for two-qubit, three-qubit and one-qutrit systems. In particular, this geometric approach allows us to construct, for the first time, closed-form expressions for the maximal magic states in the three-qubit and one-qutrit systems, and to conjecture their total counts. In the three-qubit case, we further classify the extremal magic states according to their entanglement structure. We also examine the distinctive behaviour of one-qutrit maximal magic states with respect to Clifford orbits. Our findings suggest that deep algebraic and geometric symmetries underlie the structure of extremal magic states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal Magic States from Symmetric Lattices Ohta, Misaki Sakurai, Kazuki Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics Magic, a key quantum resource beyond entanglement, remains poorly understood in terms of its structure and classification. In this paper, we demonstrate a striking connection between high-dimensional symmetric lattices and quantum magic states. By mapping vectors from the $E_8$, $BW_{16}$, and $E_6$ lattices into Hilbert space, we construct and classify stabiliser and maximal magic states for two-qubit, three-qubit and one-qutrit systems. In particular, this geometric approach allows us to construct, for the first time, closed-form expressions for the maximal magic states in the three-qubit and one-qutrit systems, and to conjecture their total counts. In the three-qubit case, we further classify the extremal magic states according to their entanglement structure. We also examine the distinctive behaviour of one-qutrit maximal magic states with respect to Clifford orbits. Our findings suggest that deep algebraic and geometric symmetries underlie the structure of extremal magic states. |
| title | Extremal Magic States from Symmetric Lattices |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.11725 |