Robustness of Magic and the Directed Geometry of State Conversion
Abstract
In this work, we introduce a state-space distance calibrated by stabilizer states based on the dual structure of the robustness of magic (RoM), and show that RoM is exactly represented as the distance to the free-state set. We then extend this geometry to state conversion by defining the directed conversion deficiency Cℱ as the distance between a target state and the set of states freely reachable from a given input state. The quantity Cℱ characterizes free convertibility and is related to the minimum stabilizer quasiprobability weight required to represent the conversion residual through the relation 1+2Cℱ. It also contains the conventional magic state resource lower bounds based on RoM and can detect stronger conversion obstructions. For single-qubit systems, we analytically construct a continuous family of mixed states with identical RoM but asymmetric convertibility.
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BibTeX
@misc{kanno2026robustness,
title = {{Robustness of Magic and the Directed Geometry of State Conversion}},
author = {Satoshi Kanno and Yoshi-aki Shimada},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38401},
eprint = {2610.38401},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38401},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robustness of Magic and the Directed Geometry of State Conversion
AU - Satoshi Kanno
AU - Yoshi-aki Shimada
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38401
UR - https://arxiv.org/abs/2610.38401
AB - In this work, we introduce a state-space distance calibrated by stabilizer states based on the dual structure of the robustness of magic (RoM), and show that RoM is exactly represented as the distance to the free-state set. We then extend this geometry to state conversion by defining the directed conversion deficiency C_ℱ as the distance between a target state and the set of states freely reachable from a given input state. The quantity C_ℱ characterizes free convertibility and is related to the minimum stabilizer quasiprobability weight required to represent the conversion residual through the relation 1+2C_ℱ. It also contains the conventional magic state resource lower bounds based on RoM and can detect stronger conversion obstructions. For single-qubit systems, we analytically construct a continuous family of mixed states with identical RoM but asymmetric convertibility.
ER -