  While local unitary transformations are used for identifying quantum states
which are in the same topological class, non-local unitary transformations are
also important for studying the transition between different topological
classes. In particular, it is an important task to find suitable non-local
transformations that systematically sweep different topological classes. Here,
regarding the role of dimension in the topological classes, we introduce
partially local unitary transformations namely Greenberger-Horne-Zeilinger
(GHZ) disentanglers which reduce the dimension of the initial topological model
by a layer-by-layer disentangling mechanism. We apply such disentanglers to
two-dimensional (2D) topological quantum codes and show that they are converted
to many copies of Kitaev's ladders. It implies that the GHZ disentangler causes
a transition from an intrinsic topological phase to a symmetry-protected
topological phase. Then, we show that while Kitaev's ladders are building
blocks of both color code and toric code, there are different patterns of
entangling ladders in 2D color code and toric code. It shows that different
topological features of these topological codes are reflected in different
patterns of entangling ladders. In this regard, we propose that the
layer-by-layer disentangling mechanism can be used as a systematic method for
classification of topological orders based on finding different patterns of the
long-range entanglement in topological lattice models.
