The most entangled states of four and seven qubits

arXiv:2611.05757v1 Announce Type: new Abstract: Pure states of four and seven qubits cannot be maximally entangled across every balanced bipartition; we determine how entangled they can be on average. For four qubits we prove the conjecture of Higuchi and Sudbery: the mean von Neumann entropy of the three $2|2$ cuts is at most $1+\tfrac12\log_2 3$ bits, with equality exactly on the local-unitary orbits of their state $M_4$ and its complex conjugate. For seven qubits the mean purity of the 35 balanced $3|4$ cuts is at least $121/917$ and their mean entropy is at most $2.965356029\ldots$ bits, each with a unique optimiser up to local unitaries and qubit permutations.