Stabilizer entropies and nonstabilizerness monotones

Tobias Haug; Lorenzo Piroli

doi:10.22331/q-2023-08-28-1092

Stabilizer entropies and nonstabilizerness monotones

Tobias Haug¹ and Lorenzo Piroli²

¹QOLS, Blackett Laboratory, Imperial College London SW7 2AZ, UK
²Philippe Meyer Institute, Physics Department, École Normale Supérieure (ENS), Université PSL, 24 rue Lhomond, F-75231 Paris, France

Published:	2023-08-28, volume 7, page 1092
Eprint:	arXiv:2303.10152v2
Doi:	https://doi.org/10.22331/q-2023-08-28-1092
Citation:	Quantum 7, 1092 (2023).

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Abstract

We study different aspects of the stabilizer entropies (SEs) and compare them against known nonstabilizerness monotones such as the min-relative entropy and the robustness of magic. First, by means of explicit examples, we show that, for Rényi index $0\leq n\leq2$, the SEs are not monotones with respect to stabilizer protocols which include computational-basis measurements, not even when restricting to pure states (while the question remains open for $n\geq2$). Next, we show that, for any Rényi index, the SEs do not satisfy a strong monotonicity condition with respect to computational-basis measurements. We further study SEs in different classes of many-body states. We compare the SEs with other measures, either proving or providing numerical evidence for inequalities between them.
Finally, we discuss exact or efficient tensor-network numerical methods to compute SEs of matrix-product states (MPSs) for large numbers of qubits. In addition to previously developed exact methods to compute the Rényi SEs, we also put forward a scheme based on perfect MPS sampling, allowing us to compute efficiently the von Neumann SE for large bond dimensions.

► BibTeX data

@article{Haug2023stabilizerentropies,
  doi = {10.22331/q-2023-08-28-1092},
  url = {https://doi.org/10.22331/q-2023-08-28-1092},
  title = {Stabilizer entropies and nonstabilizerness monotones},
  author = {Haug, Tobias and Piroli, Lorenzo},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1092},
  month = aug,
  year = {2023}
}

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