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Distinguishing non-local orders, including global and topological orders ofstates through solely local measurements and classical communications (LOCC) isa highly non-trivial and challenging task since the topology of states isdetermined by the global characteristics of the many-body system, such as thesystem's symmetry and the topological space it is based on. Here we report thatwe reproduced the phase diagram of Ising model and symmetry protectedtopological (SPT) phases using the quantum energy teleportation protocol, whichforesees non-trivial energy transfer between remote observers using theentanglement nature of the ground state and LOCC. The model we use includes theHaldane model, the AKLT model and the Kitaev model. Therefore our method pavesa new general experimental framework to determine and quantify phasetransitions in various condensed matter physics and statistical mechanics.

avs quantum science

Investigating global and topological order of states by local  measurement and classical communication: Study on SPT phase diagrams by  quantum energy teleportation