Extremal Magic States from Symmetric Lattices

• URL: http://arxiv.org/abs/2506.11725v1
• Date: Fri, 13 Jun 2025 12:39:40 GMT
• Title: Extremal Magic States from Symmetric Lattices
• Abstract summary: We show a striking connection between high-dimensional symmetric lattices and quantum magic states.<n>We construct and classify stabiliser and maximal magic states for two-qubit, three-qubit and one-qutrit systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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