For the maximally mixed state, aggressive truncation, Riemannian gauge optimization, and the analytic disentangler V = e^{-i蠁}U each reduce a sub-optimal LPDO representation to the minimal 蠂 = 1 bond dimension.
This is due to the fact that given a representation, one could generate multiple equivalent representations by in- serting isometries into the virtual饾湌-indices
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Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries
For the maximally mixed state, aggressive truncation, Riemannian gauge optimization, and the analytic disentangler V = e^{-i蠁}U each reduce a sub-optimal LPDO representation to the minimal 蠂 = 1 bond dimension.