Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond

• URL: http://arxiv.org/abs/2307.08258v4
• Date: Tue, 26 Nov 2024 05:35:42 GMT
• Title: Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
• Authors: Roberto Rubboli, Ryuji Takagi, Marco Tomamichel,
• Abstract summary: We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron.
• Score: 7.988085110283119
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $\alpha$-$z$ R\'enyi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation.

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