diff --git a/ignite/metrics/maximum_mean_discrepancy.py b/ignite/metrics/maximum_mean_discrepancy.py
index e0a18362b36..d92dd5448ce 100644
--- a/ignite/metrics/maximum_mean_discrepancy.py
+++ b/ignite/metrics/maximum_mean_discrepancy.py
@@ -78,7 +78,7 @@ class MaximumMeanDiscrepancy(Metric):
            1.0726975202560425
     """
 
-    _state_dict_all_req_keys = ("_sum_of_mmd2", "_num_batches")
+    _state_dict_all_req_keys = ("_xx_sum", "_yy_sum", "_xy_sum", "_num_batches")
 
     def __init__(
         self, var: float = 1.0, output_transform: Callable = lambda x: x, device: torch.device = torch.device("cpu")
@@ -130,7 +130,7 @@ def update(self, output: Sequence[torch.Tensor]) -> None:
 
         self._num_batches += 1
 
-    @sync_all_reduce("_sum_of_mmd2", "_num_batches")
+    @sync_all_reduce("_xx_sum", "_yy_sum", "_xy_sum", "_num_batches")
     def compute(self) -> float:
         if self._num_batches == 0:
             raise NotComputableError("MaximumMeanDiscrepacy must have at least one batch before it can be computed.")