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arXiv · 1608.06228

Absolutely maximally entangled states of seven qubits do not exist

Felix Huber·Otfried Gühne·Jens Siewert
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Abstract

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.

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Felix Huber, Otfried Gühne, Jens Siewert. 2017-05-18. Absolutely maximally entangled states of seven qubits do not exist. https://doi.org/10.1103/physrevlett.118.200502

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