diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
index 8b11860d0eb87..7804aec263d0f 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/plans/physical/partitioning.scala
@@ -1022,6 +1022,11 @@ case class KeyedShuffleSpec(
         } else {
           left.isSameFunction(right)
         }
+      case (_: AttributeReference, _: TransformExpression) |
+           (_: TransformExpression, _: AttributeReference) =>
+        SQLConf.get.v2BucketingPushPartValuesEnabled &&
+          !SQLConf.get.v2BucketingPartiallyClusteredDistributionEnabled &&
+          SQLConf.get.v2BucketingAllowCompatibleTransforms
       case _ => false
     }
 
@@ -1042,10 +1047,25 @@ case class KeyedShuffleSpec(
    * @param other other key-grouped shuffle spec
    */
   def reducers(other: KeyedShuffleSpec): Option[Seq[Option[Reducer[_, _]]]] = {
-     val results = partitioning.expressions.zip(other.partitioning.expressions).map {
-       case (e1: TransformExpression, e2: TransformExpression) => e1.reducers(e2)
-       case (_, _) => None
-     }
+    val results = partitioning.expressions.zip(other.partitioning.expressions).map {
+      case (e1: TransformExpression, e2: TransformExpression) => e1.reducers(e2)
+
+      // Identity transform on this side, arbitrary transform on the other side: create a reducer
+      // that applies the other's transform to the raw identity values. The symmetric case
+      // (TransformExpression, AttributeReference) is handled when the other side calls reducers.
+      // Each partition expression is guaranteed to have exactly one leaf child (asserted in
+      // keyPositions), so `a` lives at position 0 in the row we construct.
+      case (a: AttributeReference, t: TransformExpression) =>
+        val reducerExpr = t.transform { case _: AttributeReference => a }
+        val boundExpr = BindReferences.bindReference(reducerExpr, AttributeSeq(Seq(a)))
+        Some(new Reducer[Any, Any] {
+          override def reduce(v: Any): Any = boundExpr.eval(new GenericInternalRow(Array[Any](v)))
+          override def resultType(): DataType = reducerExpr.dataType
+          override def displayName(): String = reducerExpr.toString
+        })
+
+      case (_, _) => None
+    }
 
     // optimize to not return a value, if none of the partition expressions are reducible
     if (results.forall(p => p.isEmpty)) None else Some(results)
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala b/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala
index 21661c8a90574..688196b47502e 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/connector/KeyGroupedPartitioningSuite.scala
@@ -3528,4 +3528,44 @@ class KeyGroupedPartitioningSuite extends DistributionAndOrderingSuiteBase with
       }
     }
   }
+
+  test("SPARK-56182: Reduce identity to other transforms") {
+    val items_partitions = Array(bucket(4, "id"))
+    createTable(items, itemsColumns, items_partitions)
+    sql(s"INSERT INTO testcat.ns.$items VALUES " +
+      s"(0, 'aa', 39.0, cast('2020-01-01' as timestamp)), " +
+      s"(1, 'aa', 40.0, cast('2020-01-01' as timestamp)), " +
+      s"(2, 'bb', 41.0, cast('2021-01-03' as timestamp)), " +
+      s"(3, 'bb', 42.0, cast('2021-01-04' as timestamp))")
+
+    val purchases_partitions = Array(identity("item_id"))
+    createTable(purchases, purchasesColumns, purchases_partitions)
+    sql(s"INSERT INTO testcat.ns.$purchases VALUES " +
+      s"(3, 42.0, cast('2020-01-01' as timestamp)), " +
+      s"(0, 44.0, cast('2020-01-15' as timestamp)), " +
+      s"(1, 46.5, cast('2021-02-08' as timestamp))")
+
+    withSQLConf(
+      SQLConf.V2_BUCKETING_PUSH_PART_VALUES_ENABLED.key -> "true",
+      SQLConf.V2_BUCKETING_ALLOW_COMPATIBLE_TRANSFORMS.key -> "true") {
+      Seq(
+        s"testcat.ns.$items i JOIN testcat.ns.$purchases p ON p.item_id = i.id",
+        s"testcat.ns.$purchases p JOIN testcat.ns.$items i ON i.id = p.item_id"
+      ).foreach { joinString =>
+        val df = sql(
+          s"""
+             |${selectWithMergeJoinHint("i", "p")} id, item_id
+             |FROM $joinString
+             |ORDER BY id, item_id
+             |""".stripMargin)
+
+        val shuffles = collectShuffles(df.queryExecution.executedPlan)
+        assert(shuffles.isEmpty, "should not add shuffle for both sides of the join")
+        val groupPartitions = collectGroupPartitions(df.queryExecution.executedPlan)
+        assert(groupPartitions.forall(_.outputPartitioning.numPartitions == 4))
+
+        checkAnswer(df, Seq(Row(0, 0), Row(1, 1), Row(3, 3)))
+      }
+    }
+  }
 }