Absolutely Maximally Entangled States of Seven Qubits Do Not Exist

Pure multiparticle quantum states are called absolutely maximally entangled if all reduced states obtained by tracing out at least half of the particles are maximally mixed. We provide a method to characterize these states for a general multiparticle system. With that, we prove that a seven-qubit st...

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Bibliographic Details
Published in:Physical review letters 2017-05, Vol.118 (20), p.200502-200502, Article 200502
Main Authors: Huber, Felix, Gühne, Otfried, Siewert, Jens
Format: Article
Language:English
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Summary:Pure multiparticle quantum states are called absolutely maximally entangled if all reduced states obtained by tracing out at least half of the particles are maximally mixed. We provide a method to characterize these states for a general multiparticle system. With that, we prove that a seven-qubit state whose three-body marginals are all maximally mixed, or equivalently, a pure ((7,1,4))_{2} quantum error correcting code, does not exist. Furthermore, we obtain an upper limit on the possible number of maximally mixed three-body marginals and identify the state saturating the bound. This solves the seven-particle problem as the last open case concerning maximally entangled states of qubits.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.118.200502