Non-local Magic: closed-form solution and equivalence with magic of purification

• URL: http://arxiv.org/abs/2609.04119v1
• Date: Thu, 03 Sep 2026 17:21:11 GMT
• Title: Non-local Magic: closed-form solution and equivalence with magic of purification
• Abstract summary: Non-local magic quantifies the non-stabilizerness of a bipartite quantum state that cannot be removed by local unitary transformations.<n>We introduce the magic of purification, defined as the minimum pure-state magic over all purifications of a mixed state.<n>We prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator.
• Score: 0.9481925300137773
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-local magic quantifies the non-stabilizerness of a bipartite quantum state that cannot be removed by local unitary transformations. Despite its natural definition, its evaluation generally requires a difficult optimization over local unitaries. Here, we show that for the log-stabilizer fidelity this optimization admits an exact closed-form analytic solution depending only on the Schmidt spectrum. We then introduce the magic of purification, defined as the minimum pure-state magic over all purifications of a mixed state, and show that it naturally induces a resource theory whose free states are normalized stabilizer-code projectors. For the log-stabilizer fidelity, the magic of purification admits a distance-based formulation in terms of the Uhlmann fidelity. Remarkably, we prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator. Our results provide both an efficient analytical characterization and a mixed-state resource-theoretic interpretation of non-local magic.

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