Robustness of a state with Ising topological order against local projective measurements
arXiv:2403.07866 · doi:10.1103/PhysRevB.110.L161111
Abstract
We investigate the fragility of a topologically ordered state, namely, the ground state of a weakly Zeeman perturbed honeycomb Kitaev model to environment induced decoherence effects mimicked by random local projective measurements. Our findings show the nonabelian Ising topological order, as quantified by a tripartite mutual information (the topological entanglement entropy ,) is resilient to such disturbances. Further, is found to evolve smoothly from a topologically ordered state to a distribution of trivial states as a function of rate of measurement (temperature). We assess our model by contrasting it with the Toric Code limit of the Kitaev model, whose ground state has abelian topological order, and which has garnered greater attention in the literature of fault-tolerant quantum computation. The findings reveal the topological order in the Toric Code limit collapses rapidly as opposed to our model where it can withstand higher measurement rates.
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