bibkey: brierleyhiguchi2007fourqubit authors: S. Brierley; A. Higuchi year: 2007 title: “On maximal entanglement between two pairs in four-qubit pure states” doi: 10.1088/1751-8113/40/29/016 url: https://arxiv.org/abs/0704.2961v2 claim: “Four-qubit marginal entropy: the Higuchi–Sudbery candidate, its known restrictions, and the unrestricted maximum question.” strata_touched:

• D5/S3/Quantum/Entanglement/HiguchiSudbery/HiguchiSudberyEntropyMaximum license: citation-only triage: anchor

Verified locator

DOI: https://doi.org/10.1088/1751-8113/40/29/016

Source: https://arxiv.org/abs/0704.2961v2

On maximal entanglement between two pairs in four-qubit pure states

Local maximality

Abstract, p. 1:

We show that the state with the highest known average two-particle von Neumann entanglement entropy proposed by Sudbery and one of the authors gives a local maximum of this entropy. We also show that this is not the case for an alternative highly entangled state proposed by Brown et al.

Section 1, p. 3, distinguishes local from global maximality:

The authors of [4] conjectured that $|M_4⟩$ gives a maximum of the average two-qubit bipartite entanglement. By considering the first variation, $\delta E_{XY}$, they were able to show that $E_2$ is stationary at $|M_4⟩$. In this paper, we will consider the second variation of the average entropy and demonstrate that the state $|M_4⟩$ indeed gives a local maximum.

The candidate uses the conjugate phase on $|0110⟩$ and $|1001⟩$, which equals ${\omega }^2$ for $\omega =\exp (2i\pi /3)$. The local maximum is a literature result; the unrestricted upper bound is a separate statement.