Abstract
A pure multi-qubit state is called absolutely maximally entangled if all reduced states obtained by tracing out at least half of the particles are maximally mixed. Recently, Felix Huber proved that the absolutely maximally seven-qubit entangled state does not exist. In this letter, we investigate the relation of reduced density matrix and the local unitary transformation invariants of four- and eight-qubit entangled states. Using some constraint conditions, for four- and eight-qubit states, we can prove that absolutely maximally entangled states do not exist.
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Zhi, P., Hu, Y. Demonstrate Absolutely Maximally Entangled of Four- and Eight-qubit States Inexistence via Simple Constraint Condition. Int J Theor Phys 60, 3488–3493 (2021). https://doi.org/10.1007/s10773-021-04924-8
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DOI: https://doi.org/10.1007/s10773-021-04924-8