Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
Absolutely maximally entangled states of seven qubits do not exist
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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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Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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Graph restricted tensors: building blocks for holographic networks
Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
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Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.