Merge pull request #164 from georgios-ts/fix-is-unitary-channel

Fix `is_unitary` for channels.

tests/test_channel_props/test_is_unitary.py

@@ -3,19 +3,43 @@
 
 from toqito.channel_props import is_unitary
 from toqito.channels import depolarizing
+from toqito.perms import swap_operator
 
 
-def test_is_completely_positive_kraus_false():
+def test_is_unitary_identity_channel_true():
     """Verify that the identity channel is a unitary channel."""
     kraus_ops = [[np.identity(2), np.identity(2)]]
 
     np.testing.assert_equal(is_unitary(kraus_ops), True)
 
 
-def test_is_completely_positive_choi_true():
+def test_is_unitary_depolarizing_false():
     """Verify that the Choi matrix of the depolarizing map is not a unitary channel."""
     np.testing.assert_equal(is_unitary(depolarizing(2)), False)
 
 
+def test_is_unitary_isometry_false():
+    """Verify that an isometry is not a unitary channel."""
+    kraus_ops = [np.array([[1, 0, 0], [0, 1, 0]])]
+    np.testing.assert_equal(is_unitary(kraus_ops), False)
+
+
+def test_is_unitary_cp_channel_false():
+    """Verify that a CP channel with two kraus ops is not a unitary channel."""
+    kraus_ops = [np.identity(2), np.array([[0, 1], [1, 0]])]
+    np.testing.assert_equal(is_unitary(kraus_ops), False)
+
+
+def test_is_unitary_false():
+    """Verify that a channel with one left and right kraus ops is not a unitary channel."""
+    kraus_ops = [[np.identity(2), np.array([[0, 1], [1, 0]])]]
+    np.testing.assert_equal(is_unitary(kraus_ops), False)
+
+
+def test_is_unitary_transpose_map_false():
+    """Verify that the channel that transposes 3x2 matrices is not unitary."""
+    np.testing.assert_equal(is_unitary(swap_operator([2, 3])), False)
+
+
 if __name__ == "__main__":
     np.testing.run_module_suite()

toqito/channel_props/is_unitary.py

@@ -4,6 +4,7 @@
 import numpy as np
 
 from toqito.channel_ops import choi_to_kraus
+from toqito.matrix_props import is_unitary as is_unitary_matrix
 
 
 def is_unitary(phi: np.ndarray | list[list[np.ndarray]]) -> bool:
@@ -68,7 +69,22 @@ def is_unitary(phi: np.ndarray | list[list[np.ndarray]]) -> bool:
     # If the variable `phi` is provided as a ndarray, we assume this is a
     # Choi matrix.
     if isinstance(phi, np.ndarray):
-        phi = choi_to_kraus(phi)
-
-    # If the length of the list of krauss operarator is equal to one, the channel is unitary.
-    return len(phi) == 1
+        try:
+            phi = choi_to_kraus(phi)
+        except ValueError:
+            # if we fail to obtain a Kraus representation then input/ouput spaces might be
+            # non squares or their dimensions are not equal. Hence the channel is not unitary.
+            return False
+
+    # If there is a unique Kraus operator and it's a unitary matrix then the channel is unitary.
+    if len(phi) != 1:
+        return False
+
+    u_mat = phi[0]
+    if isinstance(phi[0], list):
+        # we enter here if phi is specified as: [[U, U]] or [[U]]
+        u_mat = phi[0][0]
+        if len(phi[0]) > 2 or (len(phi[0]) == 2 and not np.allclose(phi[0][0], phi[0][1])):
+            return False
+
+    return is_unitary_matrix(u_mat)