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- W4384647954 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 which are additive for single-qubit states and obtain much tighter upper bounds for magic state distillation. Moreover, we recover some already-known results and provide a complete picture of the additivity properties for single-qubit states for a wide class of monotones based on quantum relative entropies. We also derive a closed-form expression for all single-qubit states for the stabilizer fidelity and the generalized robustness of magic. Finally, we show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise, for which we give closed-form expressions." @default.
- W4384647954 created "2023-07-19" @default.
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- W4384647954 date "2023-07-17" @default.
- W4384647954 modified "2023-10-18" @default.
- W4384647954 title "Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond" @default.
- W4384647954 doi "https://doi.org/10.48550/arxiv.2307.08258" @default.
- W4384647954 hasPublicationYear "2023" @default.
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