diff --git a/qiskit_addon_utils/exp_vals/observable_mappings.py b/qiskit_addon_utils/exp_vals/observable_mappings.py
index 5352ad7..fcd78b4 100644
--- a/qiskit_addon_utils/exp_vals/observable_mappings.py
+++ b/qiskit_addon_utils/exp_vals/observable_mappings.py
@@ -41,10 +41,10 @@ def map_observable_isa_to_canonical(
     p_2_c = {p: c for c, p in c_2_p.items()}
 
     if isinstance(isa_observable, Pauli):
-        if isa_observable.phase != 0:
-            raise NotImplementedError("`Pauli` observable must have zero phase.")
-
-        return isa_observable[canonical_qubits]
+        obs_out = isa_observable.copy()
+        obs_out = obs_out[canonical_qubits]
+        obs_out.phase = isa_observable.phase
+        return obs_out
 
     if isinstance(isa_observable, SparsePauliOp):
         return SparsePauliOp.from_sparse_list(
diff --git "a/test/exp_vals/\\" "b/test/exp_vals/\\"
new file mode 100644
index 0000000..a504b88
--- /dev/null
+++ "b/test/exp_vals/\\"
@@ -0,0 +1,30 @@
+# This code is a Qiskit project.
+#
+# (C) Copyright IBM 2024.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Tests for coloring utilities."""
+
+import unittest
+import pytest
+from qiskit.quantum_info import Pauli
+from qiskit_addon_utils.exp_vals import map_observable_isa_to_canonical
+
+class TestObservableMapping(unittest.TestCase):
+    def test_isa_to_canonical(self):
+        with self.subTest("Pauli"):
+            obs = Pauli("IIIIZZIIII")
+            obs.phase = 3
+            canonical_qubits = [3, 4, 6, 5]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = Pauli("ZIZI")
+            target_obs.phase = 3
+            self.assertEqual(target_obs, mapped_obs)
+            self.assertEqual(target_obs.phase, mapped_obs.phase)
diff --git a/test/exp_vals/test_observable_mappings.py b/test/exp_vals/test_observable_mappings.py
new file mode 100644
index 0000000..f23648b
--- /dev/null
+++ b/test/exp_vals/test_observable_mappings.py
@@ -0,0 +1,62 @@
+# This code is a Qiskit project.
+#
+# (C) Copyright IBM 2024.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Tests for coloring utilities."""
+
+import unittest
+
+from qiskit.quantum_info import Pauli, SparseObservable, SparsePauliOp
+from qiskit_addon_utils.exp_vals import map_observable_isa_to_canonical
+
+
+class TestObservableMapping(unittest.TestCase):
+    def test_isa_to_canonical(self):
+        with self.subTest("Pauli"):
+            obs = Pauli("iIIIIZZIIII")
+            canonical_qubits = [3, 4, 6, 5]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = Pauli("iZIZI")
+            self.assertEqual(target_obs, mapped_obs)
+            self.assertEqual(target_obs.phase, mapped_obs.phase)
+        with self.subTest("SparsePauliOp"):
+            obs = SparsePauliOp(["iIZIZIZIZIZ", "iZIZIZIZIZI"], [2.0, 4.0])
+            canonical_qubits = [1, 3, 5, 7, 9, 0, 2, 4, 6, 8]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = SparsePauliOp(["iZZZZZIIIII", "iIIIIIZZZZZ"], [2.0, 4.0])
+            self.assertEqual(target_obs, mapped_obs)
+        with self.subTest("SparseObservable"):
+            obs = SparseObservable.from_list([("IZIZIZIZIZ", 2.0j), ("ZIZIZIZIZI", 4.0j)])
+            canonical_qubits = [1, 3, 5, 7, 9, 0, 2, 4, 6, 8]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = SparseObservable.from_list([("ZZZZZIIIII", 2.0j), ("IIIIIZZZZZ", 4.0j)])
+            self.assertEqual(target_obs, mapped_obs)
+
+    def test_virtual_to_canonical(self):
+        with self.subTest("Pauli"):
+            obs = Pauli("iIIIIZZIIII")
+            canonical_qubits = [3, 4, 6, 5]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = Pauli("iZIZI")
+            self.assertEqual(target_obs, mapped_obs)
+            self.assertEqual(target_obs.phase, mapped_obs.phase)
+        with self.subTest("SparsePauliOp"):
+            obs = SparsePauliOp(["iIZIZIZIZIZ", "iZIZIZIZIZI"], [2.0, 4.0])
+            canonical_qubits = [1, 3, 5, 7, 9, 0, 2, 4, 6, 8]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = SparsePauliOp(["iZZZZZIIIII", "iIIIIIZZZZZ"], [2.0, 4.0])
+            self.assertEqual(target_obs, mapped_obs)
+        with self.subTest("SparseObservable"):
+            obs = SparseObservable.from_list([("IZIZIZIZIZ", 2.0j), ("ZIZIZIZIZI", 4.0j)])
+            canonical_qubits = [1, 3, 5, 7, 9, 0, 2, 4, 6, 8]
+            mapped_obs = map_observable_isa_to_canonical(obs, canonical_qubits)
+            target_obs = SparseObservable.from_list([("ZZZZZIIIII", 2.0j), ("IIIIIZZZZZ", 4.0j)])
+            self.assertEqual(target_obs, mapped_obs)