Pauli instability in arbitrary states: detecting magic in physical correlators
Abstract
Measures of non-stabilizerness (``magic'') of a quantum evolution quantify how hard it is to simulate on a classical computer. A natural question is how to extract information about magic from physical correlators, for example at finite temperature or in the ground state. In this paper we show how to measure magic using out-of-time-order correlators evaluated in an arbitrary state. For every full-rank state, and in particular for every Gibbs state, the resulting quantity vanishes if and only if the evolution is Clifford. We establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove that, even with a single fixed probe operator, it gives a lower bound on the number of T gates needed to implement the dynamics in any circuit architecture.
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BibTeX
@misc{jackson2026pauli,
title = {{Pauli instability in arbitrary states: detecting magic in physical correlators}},
author = {Tanner Jackson and Alexey Milekhin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40032},
eprint = {2609.40032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40032},
note = {CC0},
}
RIS
TY - UNPB
TI - Pauli instability in arbitrary states: detecting magic in physical correlators
AU - Tanner Jackson
AU - Alexey Milekhin
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40032
UR - https://arxiv.org/abs/2609.40032
AB - Measures of non-stabilizerness (``magic'') of a quantum evolution quantify how hard it is to simulate on a classical computer. A natural question is how to extract information about magic from physical correlators, for example at finite temperature or in the ground state. In this paper we show how to measure magic using out-of-time-order correlators evaluated in an arbitrary state. For every full-rank state, and in particular for every Gibbs state, the resulting quantity vanishes if and only if the evolution is Clifford. We establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove that, even with a single fixed probe operator, it gives a lower bound on the number of T gates needed to implement the dynamics in any circuit architecture.
ER -