In his seminal work from 1973, Delsarte conjectured that the Johnson schemes admit no nontrivial perfect codes. We prove this fundamental conjecture which is central in combinatorial coding theory. Our arguments combine lower bounds on the design strength of a perfect code with divisibility conditions for the size of a...
T. Etzion, Xian-De Zhang, Wen-Jie Zhong· 1 citation
Absolutely maximally entangled states require every reduction of at most half of the parties to be maximally mixed, a condition that is both rigid and often impossible for qubit systems. Previous work introduced the quantum extremal number, which maximizes the number of exactly maximally mixed half-body marginals, and...
Unextendible product bases (UPBs) are important structures in quantum information theory, with applications to completely entangled subspaces, bound entanglement, and local indistinguishability. Since many properties and applications of UPBs are closely related to their cardinalities, one of the central problems in the...
Zicheng Han, Wanchen Zhang, Fei Shi et al.· 1 citation
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