diff --git a/cirq-core/cirq/ops/common_channels.py b/cirq-core/cirq/ops/common_channels.py
index 7f28231becf..08767d86258 100644
--- a/cirq-core/cirq/ops/common_channels.py
+++ b/cirq-core/cirq/ops/common_channels.py
@@ -139,7 +139,9 @@ def __repr__(self) -> str:
     def __str__(self) -> str:
         return 'asymmetric_depolarize(' + f"error_probabilities={self._error_probabilities})"
 
-    def _circuit_diagram_info_(self, args: 'protocols.CircuitDiagramInfoArgs') -> str:
+    def _circuit_diagram_info_(
+        self, args: 'protocols.CircuitDiagramInfoArgs'
+    ) -> Union[str, Iterable[str]]:
         if self._num_qubits == 1:
             if args.precision is not None:
                 return (
@@ -154,7 +156,9 @@ def _circuit_diagram_info_(self, args: 'protocols.CircuitDiagramInfoArgs') -> st
             ]
         else:
             error_probabilities = [f"{pauli}:{p}" for pauli, p in self._error_probabilities.items()]
-        return f"A({', '.join(error_probabilities)})"
+        return [f"A({', '.join(error_probabilities)})"] + [
+            f'({i})' for i in range(1, self._num_qubits)
+        ]
 
     @property
     def p_i(self) -> float:
@@ -193,13 +197,9 @@ def _json_dict_(self) -> Dict[str, Any]:
         return protocols.obj_to_dict_helper(self, ['error_probabilities'])
 
     def _approx_eq_(self, other: Any, atol: float) -> bool:
-        return (
-            self._num_qubits == other._num_qubits
-            and np.isclose(self.p_i, other.p_i, atol=atol).item()
-            and np.isclose(self.p_x, other.p_x, atol=atol).item()
-            and np.isclose(self.p_y, other.p_y, atol=atol).item()
-            and np.isclose(self.p_z, other.p_z, atol=atol).item()
-        )
+        self_keys, self_values = zip(*sorted(self.error_probabilities.items()))
+        other_keys, other_values = zip(*sorted(other.error_probabilities.items()))
+        return self_keys == other_keys and protocols.approx_eq(self_values, other_values, atol=atol)
 
 
 def asymmetric_depolarize(
diff --git a/cirq-core/cirq/ops/common_channels_test.py b/cirq-core/cirq/ops/common_channels_test.py
index 519a455a9a3..5e9a476e31d 100644
--- a/cirq-core/cirq/ops/common_channels_test.py
+++ b/cirq-core/cirq/ops/common_channels_test.py
@@ -805,6 +805,38 @@ def test_multi_asymmetric_depolarizing_channel_repr():
     )
 
 
+def test_multi_asymmetric_depolarizing_eq():
+    a = cirq.asymmetric_depolarize(error_probabilities={'I': 0.8, 'X': 0.2})
+    b = cirq.asymmetric_depolarize(error_probabilities={'II': 0.8, 'XX': 0.2})
+
+    assert not cirq.approx_eq(a, b)
+
+    a = cirq.asymmetric_depolarize(error_probabilities={'II': 0.8, 'XX': 0.2})
+    b = cirq.asymmetric_depolarize(error_probabilities={'II': 2 / 3, 'XX': 1 / 3})
+
+    assert not cirq.approx_eq(a, b)
+
+    a = cirq.asymmetric_depolarize(error_probabilities={'II': 2 / 3, 'ZZ': 1 / 3})
+    b = cirq.asymmetric_depolarize(error_probabilities={'II': 2 / 3, 'XX': 1 / 3})
+
+    assert not cirq.approx_eq(a, b)
+
+    a = cirq.asymmetric_depolarize(0.1, 0.2)
+    b = cirq.asymmetric_depolarize(error_probabilities={'II': 2 / 3, 'XX': 1 / 3})
+
+    assert not cirq.approx_eq(a, b)
+
+    a = cirq.asymmetric_depolarize(error_probabilities={'II': 0.667, 'XX': 0.333})
+    b = cirq.asymmetric_depolarize(error_probabilities={'II': 2 / 3, 'XX': 1 / 3})
+
+    assert cirq.approx_eq(a, b, atol=1e-3)
+
+    a = cirq.asymmetric_depolarize(error_probabilities={'II': 0.667, 'XX': 0.333})
+    b = cirq.asymmetric_depolarize(error_probabilities={'XX': 1 / 3, 'II': 2 / 3})
+
+    assert cirq.approx_eq(a, b, atol=1e-3)
+
+
 def test_multi_asymmetric_depolarizing_channel_str():
     assert str(cirq.asymmetric_depolarize(error_probabilities={'II': 0.8, 'XX': 0.2})) == (
         "asymmetric_depolarize(error_probabilities={'II': 0.8, 'XX': 0.2})"
@@ -814,16 +846,16 @@ def test_multi_asymmetric_depolarizing_channel_str():
 def test_multi_asymmetric_depolarizing_channel_text_diagram():
     a = cirq.asymmetric_depolarize(error_probabilities={'II': 2 / 3, 'XX': 1 / 3})
     assert cirq.circuit_diagram_info(a, args=no_precision) == cirq.CircuitDiagramInfo(
-        wire_symbols=('A(II:0.6666666666666666, XX:0.3333333333333333)',)
+        wire_symbols=('A(II:0.6666666666666666, XX:0.3333333333333333)', '(1)')
     )
     assert cirq.circuit_diagram_info(a, args=round_to_6_prec) == cirq.CircuitDiagramInfo(
-        wire_symbols=('A(II:0.666667, XX:0.333333)',)
+        wire_symbols=('A(II:0.666667, XX:0.333333)', '(1)')
     )
     assert cirq.circuit_diagram_info(a, args=round_to_2_prec) == cirq.CircuitDiagramInfo(
-        wire_symbols=('A(II:0.67, XX:0.33)',)
+        wire_symbols=('A(II:0.67, XX:0.33)', '(1)')
     )
     assert cirq.circuit_diagram_info(a, args=no_precision) == cirq.CircuitDiagramInfo(
-        wire_symbols=('A(II:0.6666666666666666, XX:0.3333333333333333)',)
+        wire_symbols=('A(II:0.6666666666666666, XX:0.3333333333333333)', '(1)')
     )