Two-dimensional　quantum　walks　using　a　two-state　coin　have　simpler　experimental　implementation　than　two-dimensional　quantum　walks　using　a　four-state　coin.　However,　decoherence　occurs　inevitably　during　the　evolution　of　quantum　walks　due　to　the　coupling　between　the　quantum　systems　and　their　environment.　Thus,　it　is　interesting　to　investigate　the　robustness　against　decoherence　for　two-　and　four-state　two-dimensional　quantum　walks.　Here,　we　investigate　the　effects　of　the　decoherence　on　two-　and　four-state　two-dimensional　quantum　walks　produced　by　the　broken-link-type　noise　and　compare　their　robustness　against　the　broken-link-type　noise.　Specifically,　we　analyze　the　quantum　correlation　between　the　two　spatial　dimensions　x　and　y　by　using　measurement-induced　disturbance　for　the　two-state　quantum　walks,　i.e.　the　alternate　walk　and　the　Pauli　walk,　and　the　four-state　quantum　walks,　i.e.　the　Grover,　Hadamard　and　Fourier　walks,　respectively.　Our　analysis　shows　that　the　two-state　walks　are　more　robust　against　the　broken-link-type　noise　than　the　four-state　walks.