bibkey: vidaltarrach1999robustness authors: Guifré Vidal and Rolf Tarrach year: 1999 title: “Robustness of entanglement” doi: 10.1103/PhysRevA.59.141 url: https://doi.org/10.1103/PhysRevA.59.141 claim: “Eq. (41): the random robustness of a pure state with Schmidt coefficients a₁ ≥ a₂ ≥ … relative to the maximally mixed state is n₁n₂a₁a₂.” strata_touched:
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Source: https://doi.org/10.1103/PhysRevA.59.141
DOI: 10.1103/PhysRevA.59.141 (Phys. Rev. A 59, 141–155). Text read from https://arxiv.org/abs/quant-ph/9806094, printed p. 15, Eq. (41):
its random robustness is (Appendix B) R(Ψ|| 1/(n₁n₂) I) = n₁n₂a₁a₂,
for a pure state Ψ with Schmidt coefficients {a_i}, i = 1, …, min(n₁, n₂), where a₁ and a₂ are the two largest. Since 2a₁a₂ ≤ a₁² + a₂² ≤ 1, the random robustness is at most n₁n₂/2, so |Ψ⟩⟨Ψ| + ½ I is separable and so is I + 2|Ψ⟩⟨Ψ|. The paper’s construction uses the Schmidt form.