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This research establishes an exact closed-form solution for non-local magic in bipartite quantum states, eliminating the need for complex optimization over local unitaries by relying solely on the Schmidt spectrum. By introducing "magic of purification," the study provides a distance-based formulation using Uhlmann fidelity and proves its equivalence to non-local magic within a specific resource theory framework. These findings offer an efficient analytical characterization for quantifying stabilizer resources, which is critical for advancing quantum error correction and fault-tolerant computing protocols.
Non-local Magic: closed-form solution and equivalence with magic of purification
arXiv:2609.04119v1 Announce Type: new 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.
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.
arXiv:2609.04119 [quant-ph]
(or arXiv:2609.04119v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.04119 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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