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Consider the unique ground state $|\psi\rangle$ of Kitaev's toric code model on a sphere. Has it been rigorously proved that $|\psi\rangle$ cannot be transformed into a trivial product state by ANY local unitary transformation?

This might seem obvious for physicists, as there are lots of non-trivial behavior of toric code model distinct from symmetry breaking phases. But when it comes to rigorous proof, it seems hard to rule out all possible local unitary transformations. So could it be proved rigorously?

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I believe this paper answers the question in a rigorous manner: https://arxiv.org/abs/1407.2926

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