The Pareto Frontiers of Magic and Entanglement: The Case of Two Qubits

• URL: http://arxiv.org/abs/2603.24902v1
• Date: Thu, 26 Mar 2026 00:32:43 GMT
• Title: The Pareto Frontiers of Magic and Entanglement: The Case of Two Qubits
• Abstract summary: We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement.<n>We derive simple analytical formulas for all these cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.
• Score: 35.45038676601954
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, $M_2$, and entanglement by the concurrence $Δ$. We find that the Pareto frontier of maximal magic $M_2^{(max)}(Δ)$ is composed of three separate segments, while the boundary of minimal magic $M_2^{(min)}(Δ)$ is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.

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