Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (ELOCC) are studied. We propose an alternative method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground-state local convertibility in the one-dimensional transverse field Ising model, $XY$ model and $XXZ$ model. It is found that the ELOCC convertibility suddenly changes at the phase transition points. In the transverse field Ising model the ELOCC convertibility between the first-excited state and the ground state are also distinct for different phases. The relation between the order of quantum phase transitions and the local convertibility is discussed.

• Received 16 November 2011

DOI:https://doi.org/10.1103/PhysRevA.85.022338