bibkey: liluozhang2025fisherdiscord
authors: H. Li, S. Luo, Y. Zhang
year: 2025
title: "Fisher discord as a quantifier of quantum complexity"
doi: 10.1103/6kv3-hr92
url: https://arxiv.org/abs/2510.15375v1
claim: "Section VI asks whether Fisher discord, the difference between symmetric-logarithmic-derivative Fisher information and Wigner–Yanase skew information, does not increase under partial trace."
strata_touched:
  - D5/S3/Quantum/Information/FisherDiscord/Defs
  - D5/S3/Quantum/Information/FisherDiscord/Spectral
  - D5/S3/Quantum/Information/FisherDiscord/Extension
  - D5/S3/Quantum/Information/FisherDiscord/Result
license: citation-only
triage: anchor

Fisher discord as a quantifier of quantum complexity

H. Li, S. Luo and Y. Zhang, arXiv:2510.15375v1. Published as Fisher discord as a quantifier of quantum metrological complexity, Phys. Rev. A 114, 032449 (2026), DOI 10.1103/6kv3-hr92.

Equations (6), (7) and (10) define $I_F(\rho ,H)=\frac{1}{4}\mathrm{tr}(\rho L^2)$, $i[\rho ,H]=\frac{1}{2}(L\rho +\rho L)$, $I_W(\rho ,H)=-\frac{1}{2}\mathrm{tr}[\sqrt{\rho },H{]}^2$, and $C=I_F-I_W$. The Hermitian SLD may be nonunique on the kernel; the information value is independent of that freedom.

Section VI (Summary), verbatim:

Both the quantum Fisher information based on the symmetric logarithmic derivative and the skew information does not increase under the partial traces, that is, I_F(ρ₁₂, H ⊗ 1) ≥ I_F(ρ₁, H), I_W(ρ₁₂, H ⊗ 1) ≥ I_W(ρ₁, H) … It is natural to consider such an open question: Whether quantum Fisher discord C(ρ₁₂, H ⊗ 1) = I_F(ρ₁₂, H ⊗ 1) − I_W(ρ₁₂, H ⊗ 1) for bipartite states does not increase under the partial trace.

The source establishes separate monotonicity of the two information quantities, positivity of their difference, pure-state vanishing and direct-sum additivity. Its partial-trace question concerns monotonicity of the difference.

Verified locator

• DOI: https://doi.org/10.1103/6kv3-hr92 (Phys. Rev. A 114, 032449 (2026)).
• URL: https://arxiv.org/abs/2510.15375v1 (§VI Summary, the partial-trace question; §II, definitions (6) and (7); §III, definition (10)).