Update measurements.py (#6352)

**Context:**
revert the abstract deco for StateMeasurement.process_density_matrix to
avoid unwanted conflicts for any downstreaming implementation.
**Description of the Change:**

**Benefits:**

**Possible Drawbacks:**

**Related ShortCut Story:**
[sc-75238]

pennylane/devices/tests/test_measurements.py

@@ -1757,9 +1757,6 @@ class MyMeasurement(StateMeasurement):
             def process_state(self, state, wire_order):
                 return 1
 
-            def process_density_matrix(self, density_matrix, wire_order):
-                return 1
-
         @qml.qnode(dev)
         def circuit():
             qml.X(0)
@@ -1781,9 +1778,6 @@ class MyMeasurement(StateMeasurement):
             def process_state(self, state, wire_order):
                 return 1
 
-            def process_density_matrix(self, density_matrix, wire_order):
-                return 1
-
         @qml.qnode(dev)
         def circuit():
             qml.X(0)

pennylane/measurements/measurements.py

@@ -655,7 +655,6 @@ def process_state(self, state: Sequence[complex], wire_order: Wires):
                 dimension :math:`2^n` acts on a subspace of :math:`n` wires
         """
 
-    @abstractmethod
     def process_density_matrix(self, density_matrix: TensorLike, wire_order: Wires):
         """
         Process the given density matrix.
@@ -670,6 +669,7 @@ def process_density_matrix(self, density_matrix: TensorLike, wire_order: Wires):
                 the mapping of matrix dimensions to physical qubits, allowing the function to correctly
                 trace out the subsystems not involved in the measurement or operation.
         """
+        raise NotImplementedError
 
 
 class MeasurementTransform(MeasurementProcess):

tests/measurements/test_measurements.py

@@ -621,9 +621,6 @@ class MyMeasurement(StateMeasurement):
             def process_state(self, state, wire_order):
                 return qml.math.sum(state)
 
-            def process_density_matrix(self, density_matrix, wire_order):
-                return 1
-
             @property
             def return_type(self):
                 return State
@@ -646,9 +643,6 @@ class MyMeasurement(StateMeasurement):
             def process_state(self, state, wire_order):
                 return qml.math.sum(state)
 
-            def process_density_matrix(self, density_matrix, wire_order):
-                return 1
-
             @property
             def return_type(self):
                 return State
@@ -667,6 +661,19 @@ def circuit():
         ):
             circuit()
 
+    def test_state_measurement_process_density_matrix_not_implemented(self):
+        """Test that the process_density_matrix method of StateMeasurement raises
+        NotImplementedError."""
+
+        class MyMeasurement(StateMeasurement):
+            def process_state(self, state, wire_order):
+                return qml.math.sum(state)
+
+        with pytest.raises(NotImplementedError):
+            MyMeasurement().process_density_matrix(
+                density_matrix=qml.math.array([[1, 0], [0, 0]]), wire_order=Wires([0, 1])
+            )
+
 
 class TestMeasurementTransform:
     """Tests for the MeasurementTransform class."""

tests/measurements/test_measurements_legacy.py

@@ -107,9 +107,6 @@ class MyMeasurement(StateMeasurement):
             def process_state(self, state, wire_order):
                 return qml.math.sum(state)
 
-            def process_density_matrix(self, density_matrix, wire_order):
-                return qml.math.sum(density_matrix)
-
         dev = qml.device("default.mixed", wires=2)
 
         @qml.qnode(dev)
@@ -125,9 +122,6 @@ class MyMeasurement(StateMeasurement):
             def process_state(self, state, wire_order):
                 return qml.math.sum(state)
 
-            def process_density_matrix(self, density_matrix, wire_order):
-                return qml.math.sum(density_matrix)
-
         dev = qml.device("default.mixed", wires=2, shots=1000)
 
         @qml.qnode(dev)