Local Convertibility as a Signature of Quantum Phase Transition

Department of Physics, National University of Singapore, Republic of Singapore(Dated: October28,2011)Theobservationthatconceptsfromquantuminformationhasgeneratedmanyalternativeindica-tors of quantum phase transitions hints that quantum phase transitions could possess operationalsignificance with respect to the processing of quantum information. Yet, there has remained fewstudies on whether the different quantum phases that result from such transitions differ in theircapacitytoprocessinformation. Weshowthereexistsquantumphasetransitionsthatcauseadis-tinctqualitativechangeinourabilitytosimulatecertainquantumsystemsunderperturbationofanexternalfieldbylocaloperationsandclassicalcommunication. Inparticular,bystudyingthegen-eralXY modelweshowthatincertainquantumphases,theeffectofadiabaticperturbationsoftheexternalmagneticfieldcanbesimulatedbylocalspinoperations,whereastheresultingeffectwithinotherphasesresultsinfundamentallynon-localinteractions. Wediscussthepotentialimplicationsof such phase transitions to adiabatic quantum computation, where a computational advantageexistsonlywhenadiabaticperturbationofgroundstatesresultsinmulti-bodyinteractions.