Fundamental bound on Wigner negativity generation from environmental collisions

@misc{layton2026fundamental,
  title = {{Fundamental bound on Wigner negativity generation from environmental collisions}},
  author = {Isaac Layton and Takahiro Sagawa and Ken Funo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32315},
  eprint = {2610.32315},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32315},
}

TY  - UNPB
TI  - Fundamental bound on Wigner negativity generation from environmental collisions
AU  - Isaac Layton
AU  - Takahiro Sagawa
AU  - Ken Funo
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32315
UR  - https://arxiv.org/abs/2610.32315
AB  - Beyond quadratic potentials, classical evolution laws are typically thought to arise from quantum theory as an approximate description. Here we show that classical evolution laws can emerge exactly, provided the environment interacts with the system via collisions. We use this to derive an inequality that lower bounds the distribution of environmental momentum kicks by the absolute value of the Fourier transform of the potential. We show that violating this inequality is necessary and sufficient for a non-quadratic potential to generate negativity from the set of positive Wigner functions. A simple consequence of this is a lower bound on the heating rate for a quantum system to evolve effectively classically. We illustrate our results using the theory of a levitated nanoparticle subject to photon recoil and background gas collisions. We derive the strength of external potential needed to generate Wigner negative states in an optical tweezer and propose an experimental test of whether a nanoparticle in an optical lattice is operating in a non-classical regime.
ER  -