bibkey: tarabunga2025asymmetry
authors: Poetri Sonya Tarabunga; Martina Frau; Tobias Haug; Emanuele Tirrito; Lorenzo Piroli
year: 2025
title: "A nonstabilizerness monotone from stabilizerness asymmetry"
doi: 10.1088/2058-9565/adfd0d
url: "https://arxiv.org/abs/2411.05766v1"
claim: "The paper defines the basis-minimized stabilizerness asymmetry, a Rényi entropy of stabilizer-basis measurement outcomes minimized over stabilizer bases, proves its monotonicity properties, computes it by a branch-and-bound method whose lower bound it proves for integer Rényi index above one, and conjectures that the lower bound remains valid for the Shannon entropy."
strata_touched:
  - D5/S3/Quantum/Magic/StabilizerAsymmetryShannonBoundRefutation
license: citation-only
triage: anchor

Tarabunga, Frau, Haug, Tirrito and Piroli, A nonstabilizerness monotone from stabilizerness asymmetry

P. S. Tarabunga, M. Frau, T. Haug, E. Tirrito and L. Piroli, Quantum Science and Technology 10(4) (2025) 045026, DOI 10.1088/2058-9565/adfd0d; arXiv:2411.05766v1. Quotations are from the arXiv v1 TeX source.

Section V.C writes an $N$-qubit stabilizer state in the standard form $2^{-k/2}{\sum }_x(-1{)}^{x^{\top }Qx}{i}^{c^{\top }x}|Rx+t⟩$ with $Q=Q_{\mathrm{d}}+Q^{\prime }$ upper triangular, $R$ of rank $k$ and $t\in {\mathbb{F}}_2^N/\mathrm{Im}R$. For fixed $Q^{\prime },c,R$ the states indexed by $(Q_{\mathrm{d}},t)$ form an orthonormal basis, and $p_{Q^{\prime },c,R}(Q_{\mathrm{d}},t)$ is the distribution of squared overlaps with a state $\psi$; $q_R$ is the same distribution with $Q^{\prime }=0$, $c=0$ for the state ${\psi }^{\prime }$ of absolute amplitudes. Eq. (69), proved for integer $\alpha >1$, states ${\min }_{Q^{\prime },c}{S}_{\alpha }(p_{Q^{\prime },c,R})\ge S_{\alpha }(q_R)$. The section continues:

Note that, while we are unable to prove Eq. (69) for the case $\alpha =1$, we conjecture that the lower bound remains valid, as we have not found any counter-examples.

Verified locator

Source: https://arxiv.org/abs/2411.05766v1

• DOI: https://doi.org/10.1088/2058-9565/adfd0d (journal version; title, authors, journal, volume, issue and article number (the page field) from Crossref; the journal text was not read).
• URL: https://arxiv.org/abs/2411.05766v1. The e-print member draft.tex has 1216 lines and md5 3972b4e08038d87ddf28211e09c89fdc. Locations:
  • Section V.C and the stabilizer standard form, l. 747–764;
  • the distributions $p_{Q^{\prime },c,R}$ and $q_R$, l. 769 and 776;
  • Eq. (69), l. 776–779; the conjecture for $\alpha =1$, l. 782.