Optimized discrete Wigner representations and non-stabilizerness in qubit systems
Abstract
The apparent absence of a stabilizer-specific phase-space description for qubit systems is not fundamental, but arises from fixing a state-independent discrete Wigner map. Allowing the phase-space representation to adapt to the state through a simple optimization procedure, we prove that every qubit stabilizer state admits an exact delta-function discrete Wigner representation for any fixed phase-space partition. This optimization can be implemented directly at the level of measurement statistics by selecting maximal probabilities across mutually unbiased bases forming the partition. This construction naturally leads to a non-stabilizer witness defined by the optimized value of the Wigner function at the origin. Stabilizer states saturate the universal lower bound of this witness for pure states, whereas a value strictly larger than the bound certifies non-stabilizerness. Although the witness is not a finite-size resource monotone, it becomes sharply concentrated and effectively invariant under random Clifford transformations in the large-qubit limit, suggesting an asymptotically linear growth law for broad families of non-stabilizer states. Our results restore a meaningful geometric phase-space characterization of qubit stabilizer structure and provide an operational diagnostic of non-stabilizerness.
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BibTeX
@misc{klimov2026optimized,
title = {{Optimized discrete Wigner representations and non-stabilizerness in qubit systems}},
author = {A. B. Klimov and C. Muñoz and I. Sainz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10471},
eprint = {2610.10471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10471},
}
RIS
TY - UNPB
TI - Optimized discrete Wigner representations and non-stabilizerness in qubit systems
AU - A. B. Klimov
AU - C. Muñoz
AU - I. Sainz
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.10471
UR - https://arxiv.org/abs/2610.10471
AB - The apparent absence of a stabilizer-specific phase-space description for qubit systems is not fundamental, but arises from fixing a state-independent discrete Wigner map. Allowing the phase-space representation to adapt to the state through a simple optimization procedure, we prove that every qubit stabilizer state admits an exact delta-function discrete Wigner representation for any fixed phase-space partition. This optimization can be implemented directly at the level of measurement statistics by selecting maximal probabilities across mutually unbiased bases forming the partition. This construction naturally leads to a non-stabilizer witness defined by the optimized value of the Wigner function at the origin. Stabilizer states saturate the universal lower bound of this witness for pure states, whereas a value strictly larger than the bound certifies non-stabilizerness. Although the witness is not a finite-size resource monotone, it becomes sharply concentrated and effectively invariant under random Clifford transformations in the large-qubit limit, suggesting an asymptotically linear growth law for broad families of non-stabilizer states. Our results restore a meaningful geometric phase-space characterization of qubit stabilizer structure and provide an operational diagnostic of non-stabilizerness.
ER -