Year: 2026
Type: preprint
Abstract: Quantum magic, or nonstabilizerness, is a central resource for quantum computation, motivating a systematic study of its mathematical structure and physical behavior. Here we characterize the geometry of the stabilizer polytope, obtaining near-tight bounds on its inradius, volume radius, and number of facets. These results reveal a pronounced separation between the typical presence of magic and its detectability. In particular, random mixed states obtained by tracing out an environment remain magical with high probability even when the environment contains nearly twice as many qubits as the system, demonstrating parametrically greater robustness to environmental mixing than bipartite entanglement. In contrast, commonly used magic criteria, including the Triangle and Pauli-norm-based criteria, lose detection power under much weaker mixing. More generally, when the number of environment qubits scales proportionally with the system size, certification with constant success probability requires exponentially many linear observables, even given their exact expectation values. We also prove that the number of facets of the stabilizer polytope grows doubly exponentially with the number of qubits, making exhaustive witness enumeration impractical for complete magic certification and motivating approaches that exploit the structure and symmetries of stabilizer states.
Source: arXiv (Cornell University)
Authors: Liu, Zhenhuan, Liu, Zi-Wen
Institutions: Technology Innovation Institute, Tsinghua University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G4156658221
OpenAlex ID: W7208722847