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One way to explore multiparticle entanglement is to ask for maximalentanglement with respect to different bipartitions, leading to the notion ofabsolutely maximally entangled states or perfect tensors. A different path usesunitary invariance and symmetries, resulting in the concept of multiparticlesinglet states. We show that these two concepts are incompatible in the sensethat the space of pure multiparticle singlet states does not contain any statefor which all partitions of two particles versus the rest are maximallyentangled. This puts restrictions on the construction of quantum codes andcontributes to discussions in the context of the AdS/CFT correspondence andquantum gravity.

Multiparticle singlet states cannot be maximally entangled for the bipartitions