bibkey: serranoensastiga2026monogamy authors: Eduardo Serrano-Ensástiga; Olivier Giraud; John Martin year: 2026 title: “Multiqubit monogamy relations beyond shadow inequalities” doi: 10.1103/9fkf-hm8l url: https://arxiv.org/abs/2507.12680v2 claim: “For a bipartition A|Abar of an N-qubit system into k = |A| and N - k qubits, with rho_A the reduced state of a pure state, rho~ = sigma_y^(tensor k) rho* sigma_y^(tensor k) and R_rho = Tr(rho rho~), the authors conjecture that the minimum of Tr(rho_A^2) + R_(rho_A) over pure states is 2^(k-N) if 2k > N and 2^(1-k) if 2k <= N (Conjecture 2; proved there for k = 1, numerical for 2k <= N, k >= 2).” strata_touched:
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Multiqubit monogamy relations beyond shadow inequalities
E. Serrano-Ensástiga, O. Giraud and J. Martin, arXiv:2507.12680 (v2 2026-01-07); Phys. Rev. A 113 (2026) 012415. Subject: quant-ph.
The paper derives inequalities between the sector lengths S_m of multiqubit
states. One family comes from the time-reversed state
ρ̃ = σ_y^{⊗N} ρ^* σ_y^{⊗N} and the overlap R_ρ = Tr(ρ ρ̃), evaluated on the
reduced state ρ_A of a pure state across a bipartition A | Ā with
|A| = k. Proposition 1 gives
2^{−min(k, N−k)} ≤ Tr(ρ_A²) + R_{ρ_A} ≤ (3 + (−1)^k)/2. The section on the
overlap R_ρ proves that the sum is 1 for k = 1, reports numerical minima
for N ≤ 10, and states:
Let be a bipartition of an -qubit system into and qubits. Then, the minimum of taken over all pure states of the -qubit system, is given by $\min_{|\psi\rangle} \big(\mathrm{Tr}(\rho_A^2) + R_{\rho_A}\big) = 2^{k-N}2k > N2^{-k + 1}2k \leq N$.
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- DOI: https://doi.org/10.1103/9fkf-hm8l (Crossref record; the journal text was not read).
- URL: https://arxiv.org/abs/2507.12680v2 (source
arXiv_v2.texretrieved 2026-10-01): the definitions of the time-reversed state and ofR_ρ(Sec. II), Proposition 1 (Sec. III), and Conjecture 2 at the end of Sec. V, in its subsection “The overlapR_ρ”.