bibkey: yu2017skewcoherence
authors: Chang-shui Yu
year: 2017
title: "Quantum coherence via skew information and its polygamy"
doi: 10.1103/PhysRevA.95.042337
url: https://arxiv.org/abs/1704.04871v1
claim: "The coherence C(ρ) = 1 − Σ_k ⟨k|√ρ|k⟩² defined from skew information satisfies the polygamy inequality 1 − C(Ψ_AB) ≤ [1 − C(ρ_A)][1 − C(ρ_B)] for bipartite pure states; the paper notes that the inequality fails for some two-qubit mixed states and conjectures that it holds for bipartite mixed states of dimension N ≥ 6."
strata_touched:
  - D5/S3/Quantum/Information/SkewCoherencePolygamyMixedRefutation
license: citation-only
triage: anchor

Yu, Quantum coherence via skew information and its polygamy

C.-s. Yu, Phys. Rev. A 95, 042337 (2017); arXiv:1704.04871v1. Quotations are from the v1 TeX source.

In a fixed reference basis $\{|k⟩\}$ the coherence is $C(\rho )=1-{\sum }_k⟨k|\sqrt{\rho }|k{⟩}^2$ (Lemma 1). For a bipartite pure state with reduced density matrices ${\rho }_A,{\rho }_B$, Theorem 2 gives $1-C(|\Psi {⟩}_{AB})\le [1-C({\rho }_A)][1-C({\rho }_B)]$. The paper shows that the same relation fails for some two-qubit mixed states, tests random states on $2\otimes 3$, $3\otimes 3$, $3\otimes 4$ and $4\otimes 4$, and states:

However, we would like to conjecture that it could hold for the bipartite mixed states with the dimension $N\ge 6$.

Verified locator

Source: https://arxiv.org/abs/1704.04871v1

• DOI: https://doi.org/10.1103/PhysRevA.95.042337 (Physical Review A 95(4), article 042337; title, author, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/1704.04871v1. The e-print member coherenceLy.tex has 1614 lines and md5 026b6fb07e6d276a7bd743cc480af58c. Locations:
  • the coherence, Lemma 1, l. 170–178; Theorem 2, l. 543–550;
  • the two-qubit failure and the numerical tests, l. 1370–1397 (figures at l. 1305–1323); the conjecture, l. 994–999.