Local tests of global entanglement and a counterexample to the generalized area law

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D. Aharonov, A. W. Harrow, Z. Landau, D. Nagaj, M. Szegedy, U. Vazirani
Proceedings of FOCS 2014, 246 (2014)

Maximally entangled states are a valuable resource for quantum information tasks and detecting its presence represents a very meaningful question. Can two parties test whether their joint state is maximally entangled while exchanging only a constant number of qubits? A seemingly unrelated question is the validity of the generalized area law for the growth of entanglement on ground states of quantum many body systems. Specifically, it considers lattice systems described by gapped local Hamiltonians, i.e. where only local interactions between two neighboring particles are allowed. The area law conjectures that for every bipartition of the system, the amount entanglement in the ground state is bounded by a constant times the size of the boundary of the system.

In their work, Aharonov and co-workers develop a new technique using quantum expanders that provides a definite answer for both questions. They show that, surprisingly, a constant amount of resources is sufficient to verify a global property of a bipartite quantum system, namely the state being maximally entangled. On the other hand, they disprove the generalized area law conjecture by providing a counterexample.