$|G\ra$ is a property which can not be characterized by any local order parameter. As it is shown in Fig.(\[k1\]), there are two non-trivial loops on the dual lattice and we can define two $X$-type operators corresponding to such loops, denoted by $T^1 _x$ and $T^2 _x$. Since these loop operators cross $Z$-type non-trivial loop operators once, they have an anti-commutation relation in the following form: $$\label{non}
\{T^1 _x , T^2 _z \}=0~~,~~\{T^1 _z , T^2 _x \}=0.$$ Now, if we apply operators $T^1 _x$ and $T^2 _x$ to state $|G\ra$, we obtain the four-fold degenerate ground space of the Toric code: $$\label{deg}
|\psi_{\mu \nu}\ra =(T^1 _x)^\mu (T^2 _x )^\nu |G\ra,$$ with $\mu , \nu =\{0,1\}$. Because of the anticommutation relation(\[non\]), it is concluded that the expectation values of $T^1 _z$ and $T^2 _z$ are different for the above quantum states. Since $T^1 _x$ and $T^2 _x$ are non-local operators, it means that the above quantum states can be distinguished from each other only by non-local order parameters. This property, that there is no local order parameter which can distinguish the above states from each other, is in fact the result of topological order of Toric code states. We should 