diff --git a/toqito/channel_metrics/fidelity_of_separability.py b/toqito/channel_metrics/fidelity_of_separability.py
index 0a8be9e2e..c979921b8 100644
--- a/toqito/channel_metrics/fidelity_of_separability.py
+++ b/toqito/channel_metrics/fidelity_of_separability.py
@@ -134,7 +134,7 @@ def fidelity_of_separability(
         raise ValueError("This function only works for pure states.")
 
     # We first permure psi_{BAR} to psi_{RAB} to simplify the code.
-    psi = permute_systems(psi, [3, 2, 1], psi_dims)
+    psi = permute_systems(psi, [2, 1, 0], psi_dims)
     dim_b, dim_a, dim_r = psi_dims
     psi_dims = [dim_r, dim_a, dim_b]
 
@@ -163,7 +163,7 @@ def fidelity_of_separability(
                 pi_sym
                 * picos.partial_trace(
                     (picos.partial_transpose(psi, [0], psi_dims) @ picos.I(dim_a))
-                    * permute_systems(choi_partial @ picos.I(dim_b * dim_a), [1, 4, 3, 2], dim_list),
+                    * permute_systems(choi_partial @ picos.I(dim_b * dim_a), [0, 3, 2, 1], dim_list),
                     [0, 2],
                     dim_list,
                 )
diff --git a/toqito/channel_ops/partial_channel.py b/toqito/channel_ops/partial_channel.py
index af92808bc..57f6fc90e 100644
--- a/toqito/channel_ops/partial_channel.py
+++ b/toqito/channel_ops/partial_channel.py
@@ -182,7 +182,7 @@ def partial_channel(
 
         phi_map = permute_systems(
             np.kron(np.kron(psi_r1 * psi_c1.conj().T, phi_map), psi_r2 * psi_c2.conj().T),
-            [1, 3, 5, 2, 4, 6],
+            [0, 2, 4, 1, 3, 5],
             dim,
         )
 
diff --git a/toqito/channels/partial_trace.py b/toqito/channels/partial_trace.py
index 36ba10feb..d5aa37941 100644
--- a/toqito/channels/partial_trace.py
+++ b/toqito/channels/partial_trace.py
@@ -189,10 +189,10 @@ def partial_trace(
         sys = np.array(sys)
     if isinstance(sys, int):
         sys = np.array([sys])
-    set_diff = list(set(list(range(1, num_sys + 1))) - set(sys + 1))
 
+    set_diff = list(set(list(range(num_sys))) - set(sys))
     perm = set_diff
-    perm.extend(sys + 1)
+    perm.extend(sys)
 
     a_mat = permute_systems(input_mat, perm, dim)
 
diff --git a/toqito/channels/partial_transpose.py b/toqito/channels/partial_transpose.py
index 4aebb5e2f..693b3d3b3 100644
--- a/toqito/channels/partial_transpose.py
+++ b/toqito/channels/partial_transpose.py
@@ -167,8 +167,8 @@ def partial_transpose(
     sub_sys_vec_r = prod_dim_r * np.ones(int(sub_prod_r)) / sub_prod_r
     sub_sys_vec_c = prod_dim_c * np.ones(int(sub_prod_c)) / sub_prod_c
 
-    set_diff = list(set(list(range(1, num_sys + 1))) - set(sys + 1))
-    perm = (sys + 1).tolist()[:]
+    set_diff = list(set(list(range(num_sys ))) - set(sys ))
+    perm = (sys ).tolist()[:]
     perm.extend(set_diff)
 
     # Permute the subsystems so that we just have to do the partial transpose
@@ -198,6 +198,6 @@ def partial_transpose(
     # Return the subsystems back to their original positions.
     dim[:, sys] = np.flipud(dim[:, sys])
 
-    dim = dim[:, (np.array(perm) - 1).tolist()]
+    dim = dim[:, (np.array(perm) ).tolist()]
 
     return permute_systems(z_tmp, perm, dim, False, True)
diff --git a/toqito/nonlocal_games/quantum_hedging.py b/toqito/nonlocal_games/quantum_hedging.py
index 6ae91b16d..252d45fa2 100644
--- a/toqito/nonlocal_games/quantum_hedging.py
+++ b/toqito/nonlocal_games/quantum_hedging.py
@@ -90,8 +90,8 @@ def __init__(self, q_a: np.ndarray, num_reps: int) -> None:
         # action:
         #   π(y1 ⊗ y2 ⊗ x1 ⊗ x2) = y1 ⊗ x1 ⊗ y2 ⊗ x2
         # for all y1 ∈ Y1, y2 ∈ Y2, x1 ∈ X1, x2 ∈ X2.).
-        l_1 = list(range(1, self._num_reps + 1))
-        l_2 = list(range(self._num_reps + 1, self._num_reps**2 + 1))
+        l_1 = list(range(self._num_reps ))
+        l_2 = list(range(self._num_reps , self._num_reps**2 ))
         if self._num_reps == 1:
             self._pperm = np.array([1])
         else:
diff --git a/toqito/perms/antisymmetric_projection.py b/toqito/perms/antisymmetric_projection.py
index ed176ebdd..ad059119c 100644
--- a/toqito/perms/antisymmetric_projection.py
+++ b/toqito/perms/antisymmetric_projection.py
@@ -84,7 +84,7 @@ def antisymmetric_projection(dim: int, p_param: int = 2, partial: bool = False)
     if dim < p_param:
         return np.zeros((dimp, dimp * (1 - partial)))
 
-    p_list = np.array(list(permutations(np.arange(1, p_param + 1))))
+    p_list = np.array(list(permutations(np.arange(p_param ))))
     p_fac = p_list.shape[0]
 
     anti_proj = np.zeros((dimp, dimp))
diff --git a/toqito/perms/perfect_matchings.py b/toqito/perms/perfect_matchings.py
index 1d08af4bd..fd0e8e550 100644
--- a/toqito/perms/perfect_matchings.py
+++ b/toqito/perms/perfect_matchings.py
@@ -16,14 +16,13 @@ def perfect_matchings(num: list[int] | int | np.ndarray) -> np.ndarray:
 
     Examples
     ==========
-
-    This is an example of how to generate all perfect matchings of the numbers 1, 2, 3, 4.
+    This is an example of how to generate all perfect matchings of the numbers 0, 1, 2, 3.
 
     >>> from toqito.perms import perfect_matchings
     >>> perfect_matchings(4)
-    array([[1, 2, 3, 4],
-           [1, 3, 2, 4],
-           [1, 4, 3, 2]])
+    array([[0, 1, 2, 3],
+           [0, 2, 1, 3],
+           [0, 3, 2, 1]])
 
     References
     ==========
@@ -31,13 +30,13 @@ def perfect_matchings(num: list[int] | int | np.ndarray) -> np.ndarray:
         :filter: docname in docnames
 
     :param num: Either an even integer, indicating that you would like all perfect matchings of the
-                integers 1,2, ... N, or a `list` or `np.array` containing an even number of distinct
+                integers 0, 1, ... N-1, or a `list` or `np.array` containing an even number of distinct
                 entries, indicating that you would like all perfect matchings of those entries.
     :return: An array containing all valid perfect matchings of size :code:`num`.
 
     """
     if isinstance(num, int):
-        num = np.arange(1, num + 1)
+        num = np.arange(num)
     if isinstance(num, list):
         num = np.array(num)
 
@@ -73,3 +72,4 @@ def perfect_matchings(num: list[int] | int | np.ndarray) -> np.ndarray:
         matchings = np.vstack((matchings, s_vec))
 
     return matchings
+
diff --git a/toqito/perms/permutation_operator.py b/toqito/perms/permutation_operator.py
index ba08ede62..a1d869095 100644
--- a/toqito/perms/permutation_operator.py
+++ b/toqito/perms/permutation_operator.py
@@ -27,7 +27,7 @@ def permutation_operator(
     qubits
 
     .. math::
-        P_{2, [2, 1]} =
+        P_{2, [1, 0]} =
         \begin{pmatrix}
             1 & 0 & 0 & 0 \\
             0 & 0 & 1 & 0 \\
@@ -38,13 +38,12 @@ def permutation_operator(
     Using :code:`toqito`, this can be achieved in the following manner.
 
     >>> from toqito.perms import permutation_operator
-    >>> permutation_operator(2, [2, 1])
+    >>> permutation_operator(2, [1, 0])
     array([[1., 0., 0., 0.],
            [0., 0., 1., 0.],
            [0., 1., 0., 0.],
            [0., 0., 0., 1.]])
 
-
     :param dim: The dimensions of the subsystems to be permuted.
     :param perm: A permutation vector.
     :param inv_perm: Boolean dictating if :code:`perm` is inverse or not.
@@ -54,10 +53,11 @@ def permutation_operator(
     """
     # Allow the user to enter a single number for `dim`.
     if isinstance(dim, int):
-        dim = dim * np.ones(max(perm))
+        dim = [dim] * np.ones(max(perm) + 1)
     if isinstance(dim, list):
         dim = np.array(dim)
 
     mat = sp.sparse.identity(int(np.prod(dim))) if is_sparse else np.identity(int(np.prod(dim)))
     # Swap the rows of the identity matrix appropriately.
+
     return permute_systems(mat, perm, dim, True, inv_perm)
diff --git a/toqito/perms/permute_systems.py b/toqito/perms/permute_systems.py
index df750fdd0..02ff186df 100644
--- a/toqito/perms/permute_systems.py
+++ b/toqito/perms/permute_systems.py
@@ -36,7 +36,7 @@ def permute_systems(
 
     For spaces :math:`\mathcal{A}` and :math:`\mathcal{B}` where :math:`\text{dim}(\mathcal{A}) =
     \text{dim}(\mathcal{B}) = 2` we may consider an operator :math:`X \in \mathcal{A} \otimes \mathcal{B}`. Applying the
-    `permute_systems` function with vector :math:`[2,1]` on :math:`X`, we may reorient the spaces such that :math:`X \in
+    `permute_systems` function with vector :math:`[1,0]` on :math:`X`, we may reorient the spaces such that :math:`X \in
     \mathcal{B} \otimes \mathcal{A}`.
 
     For example, if we define :math:`X \in \mathcal{A} \otimes \mathcal{B}` as
@@ -53,7 +53,7 @@ def permute_systems(
     yield the following matrix
 
     .. math::
-        X_{[2,1]} = \begin{pmatrix}
+        X_{[1,0]} = \begin{pmatrix}
             1 & 3 & 2 & 4 \\
             9 & 11 & 10 & 12 \\
             5 & 7 & 6 & 8 \\
@@ -63,7 +63,7 @@ def permute_systems(
     >>> from toqito.perms import permute_systems
     >>> import numpy as np
     >>> test_input_mat = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
-    >>> permute_systems(test_input_mat, [2, 1])
+    >>> permute_systems(test_input_mat, [1, 0])
     array([[ 1,  3,  2,  4],
            [ 9, 11, 10, 12],
            [ 5,  7,  6,  8],
@@ -71,7 +71,7 @@ def permute_systems(
 
     For spaces :math:`\mathcal{A}, \mathcal{B}`, and :math:`\mathcal{C}` where :math:`\text{dim}(\mathcal{A}) =
     \text{dim}(\mathcal{B}) = \text{dim}(\mathcal{C}) = 2` we may consider an operator :math:`X \in \mathcal{A} \otimes
-    \mathcal{B} \otimes \mathcal{C}`. Applying the :code:`permute_systems` function with vector :math:`[2,3,1]` on
+    \mathcal{B} \otimes \mathcal{C}`. Applying the :code:`permute_systems` function with vector :math:`[1,2,0]` on
     :math:`X`, we may reorient the spaces such that :math:`X \in \mathcal{B} \otimes \mathcal{C} \otimes \mathcal{A}`.
 
     For example, if we define :math:`X \in \mathcal{A} \otimes \mathcal{B} \otimes \mathcal{C}` as
@@ -93,7 +93,7 @@ def permute_systems(
     \otimes \mathcal{C}` yield the following matrix
 
     .. math::
-        X_{[2, 3, 1]} =
+        X_{[1, 2, 0]} =
         \begin{pmatrix}
             1 & 5 & 2 & 6 & 3 & 7 & 4, 8 \\
             33 & 37 & 34 & 38 & 35 & 39 & 36 & 40 \\
@@ -119,7 +119,7 @@ def permute_systems(
     ...        [57, 58, 59, 60, 61, 62, 63, 64],
     ...    ]
     ... )
-    >>> permute_systems(test_input_mat, [2, 3, 1])
+    >>> permute_systems(test_input_mat, [1, 2, 0])
     array([[ 1,  5,  2,  6,  3,  7,  4,  8],
            [33, 37, 34, 38, 35, 39, 36, 40],
            [ 9, 13, 10, 14, 11, 15, 12, 16],
@@ -145,6 +145,7 @@ def permute_systems(
     else:
         input_mat_dims = input_mat.shape
 
+
     is_vec = np.min(input_mat_dims) == 1
     num_sys = len(perm)
 
@@ -176,7 +177,7 @@ def permute_systems(
     prod_dim_r = int(np.prod(dim[0, :]))
     prod_dim_c = int(np.prod(dim[1, :]))
 
-    if sorted(perm) != list(range(1, num_sys + 1)):
+    if sorted(perm) != list(range(num_sys )):
         raise ValueError("InvalidPerm: `perm` must be a permutation vector.")
     if input_mat_dims[0] != prod_dim_r or (not row_only and input_mat_dims[1] != prod_dim_c):
         raise ValueError("InvalidDim: The dimensions specified in DIM do not agree with the size of X.")
@@ -185,6 +186,10 @@ def permute_systems(
         if input_mat.shape[0] == 1:
             input_mat = input_mat[0]
             vec_orien = 1
+        # Rather than using subtraction to generate new indices,
+        # it's better to use methods designed for handling permutations directly.
+        # This avoids the risk of negative indices and is more straightforward.
+        num_sys -= 1 # 0-indexing (Since we're using 0-indexing, we need to subtract 1 from the number of subsystems.)
         permuted_mat_1 = input_mat.reshape(dim[vec_orien, ::-1].astype(int), order="F")
         if inv_perm:
             permuted_mat = vec(np.transpose(permuted_mat_1, np.argsort(num_sys - np.array(perm[::-1])))).T
diff --git a/toqito/perms/swap.py b/toqito/perms/swap.py
index 384aae764..f6e38066d 100644
--- a/toqito/perms/swap.py
+++ b/toqito/perms/swap.py
@@ -145,7 +145,7 @@ def swap(
         raise ValueError("InvalidSys: `sys` must be a vector with exactly two elements.")
 
     # Swap the indicated subsystems.
-    perm = np.array(range(1, num_sys + 1))
+    perm = np.array(range(num_sys ))
     sys = np.array(sys) - 1
 
     perm[sys] = perm[sys[::-1]]
diff --git a/toqito/perms/symmetric_projection.py b/toqito/perms/symmetric_projection.py
index a032c7ce9..0df82e3ea 100644
--- a/toqito/perms/symmetric_projection.py
+++ b/toqito/perms/symmetric_projection.py
@@ -81,7 +81,7 @@ def symmetric_projection(dim: int, p_val: int = 2, partial: bool = False) -> [np
     if p_val == 1:
         return np.eye(dim)
 
-    p_list = np.array(list(permutations(np.arange(1, p_val + 1))))
+    p_list = np.array(list(permutations(np.arange(p_val ))))
     p_fac = math.factorial(p_val)
     sym_proj = np.zeros((dimp, dimp))
 
diff --git a/toqito/perms/tests/test_perfect_matchings.py b/toqito/perms/tests/test_perfect_matchings.py
index 432133dda..2709ca3ab 100644
--- a/toqito/perms/tests/test_perfect_matchings.py
+++ b/toqito/perms/tests/test_perfect_matchings.py
@@ -8,15 +8,15 @@
 def test_perfect_matchings_num_4():
     """All perfect matchings of size 4."""
     res = perfect_matchings(4)
-    expected_res = np.array([[1, 2, 3, 4], [1, 3, 2, 4], [1, 4, 3, 2]])
+    expected_res = np.array([[0, 1, 2, 3], [0, 2, 1, 3], [0, 3, 2, 1]])
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
 def test_perfect_matchings_num_4_list():
     """All perfect matchings of size 4 with input as list."""
-    res = perfect_matchings([1, 2, 3, 4])
-    expected_res = np.array([[1, 2, 3, 4], [1, 3, 2, 4], [1, 4, 3, 2]])
+    res = perfect_matchings([0, 1, 2, 3])
+    expected_res = np.array([[0, 1, 2, 3], [0, 2, 1, 3], [0, 3, 2, 1]])
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
@@ -35,21 +35,21 @@ def test_perfect_matchings_num_6():
 
     expected_res = np.array(
         [
-            [1, 2, 3, 4, 5, 6],
-            [1, 2, 3, 5, 4, 6],
-            [1, 2, 3, 6, 5, 4],
-            [1, 3, 2, 4, 5, 6],
-            [1, 3, 2, 5, 4, 6],
-            [1, 3, 2, 6, 5, 4],
-            [1, 4, 3, 2, 5, 6],
-            [1, 4, 3, 5, 2, 6],
-            [1, 4, 3, 6, 5, 2],
-            [1, 5, 3, 4, 2, 6],
-            [1, 5, 3, 2, 4, 6],
-            [1, 5, 3, 6, 2, 4],
-            [1, 6, 3, 4, 5, 2],
-            [1, 6, 3, 5, 4, 2],
-            [1, 6, 3, 2, 5, 4],
+            [0, 1, 2, 3, 4, 5],
+            [0, 1, 2, 4, 3, 5],
+            [0, 1, 2, 5, 4, 3],
+            [0, 2, 1, 3, 4, 5],
+            [0, 2, 1, 4, 3, 5],
+            [0, 2, 1, 5, 4, 3],
+            [0, 3, 2, 1, 4, 5],
+            [0, 3, 2, 4, 1, 5],
+            [0, 3, 2, 5, 4, 1],
+            [0, 4, 2, 3, 1, 5],
+            [0, 4, 2, 1, 3, 5],
+            [0, 4, 2, 5, 1, 3],
+            [0, 5, 2, 3, 4, 1],
+            [0, 5, 2, 4, 3, 1],
+            [0, 5, 2, 1, 4, 3]
         ]
     )
     bool_mat = np.isclose(res, expected_res)
diff --git a/toqito/perms/tests/test_permutation_operator.py b/toqito/perms/tests/test_permutation_operator.py
index a7bd831e0..9e2b1e860 100644
--- a/toqito/perms/tests/test_permutation_operator.py
+++ b/toqito/perms/tests/test_permutation_operator.py
@@ -6,28 +6,28 @@
 
 
 def test_permutation_operator_standard_swap():
-    """Generates the standard swap operator on two qubits."""
+    """Generates the standard swap operator on two qubits with zero-based indexing."""
     expected_res = np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
 
-    res = permutation_operator(2, [2, 1])
+    res = permutation_operator(2, [1, 0])
 
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
 def test_permutation_operator_standard_swap_list_dim():
-    """Generates the standard swap operator on two qubits."""
+    """Generates the standard swap operator on two qubits with zero-based indexing."""
     expected_res = np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
 
-    res = permutation_operator([2, 2], [2, 1])
+    res = permutation_operator([2, 2], [1, 0])
 
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
 def test_permutation_operator_sparse_option():
-    """Sparse swap operator on two qutrits."""
-    res = permutation_operator(3, [2, 1], False, True)
+    """Sparse swap operator on two qutrits with zero-based indexing."""
+    res = permutation_operator(3, [1, 0], False, True)
 
     expected_res = np.array(
         [
@@ -46,17 +46,17 @@ def test_permutation_operator_sparse_option():
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
-def test_permutation_operator_dim_3_perm_1_2():
-    """Test permutation operator when dim is 3 and perm is [1, 2]."""
-    res = permutation_operator(3, [1, 2])
+def test_permutation_operator_dim_3_perm_0_1():
+    """Test permutation operator when dim is 3 and perm is [0, 1] using zero-based indexing."""
+    res = permutation_operator(3, [0, 1])
     expected_res = np.identity(9)
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
-def test_permutation_operator_dim_2_perm_1_3_2():
-    """Test permutation operator when dim is 2 and perm is [1, 3, 2]."""
-    res = permutation_operator(2, [1, 3, 2])
+def test_permutation_operator_dim_2_perm_0_2_1():
+    """Test permutation operator when dim is 2 and perm is [0, 2, 1] using zero-based indexing."""
+    res = permutation_operator(2, [0, 2, 1])
     expected_res = np.array(
         [
             [
@@ -75,17 +75,17 @@ def test_permutation_operator_dim_2_perm_1_3_2():
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
-def test_permutation_operator_dim_2_2_perm_1_2():
-    """Test permutation operator when dim is [2, 2] and perm is [1, 2]."""
-    res = permutation_operator([2, 2], [1, 2])
+def test_permutation_operator_dim_2_2_perm_0_1():
+    """Test permutation operator when dim is [2, 2] and perm is [0, 1] using zero-based indexing."""
+    res = permutation_operator([2, 2], [0, 1])
     expected_res = np.identity(4)
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
-def test_permutation_operator_dim_2_2_perm_2_1():
-    """Test permutation operator when dim is [2, 2] and perm is [2, 1]."""
-    res = permutation_operator([2, 2], [2, 1])
+def test_permutation_operator_dim_2_2_perm_1_0():
+    """Test permutation operator when dim is [2, 2] and perm is [1, 0] using zero-based indexing."""
+    res = permutation_operator([2, 2], [1, 0])
     expected_res = np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
diff --git a/toqito/perms/tests/test_permute_systems.py b/toqito/perms/tests/test_permute_systems.py
index 4fe098fcd..5dcd5f316 100644
--- a/toqito/perms/tests/test_permute_systems.py
+++ b/toqito/perms/tests/test_permute_systems.py
@@ -10,19 +10,19 @@ def test_permute_systems_vec():
     test_input_mat = np.array([1, 2, 3, 4])
     expected_res = np.array([1, 3, 2, 4])
 
-    res = permute_systems(test_input_mat, [2, 1])
+    res = permute_systems(test_input_mat, [1, 0])
 
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
 
 
 def test_permute_systems_m2_m2():
-    """Permute system for perm = [2,1] and dim = [2, 2]."""
+    """Permute system for perm = [0,1] and matrix of dimension [2, 2]."""
     test_input_mat = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
 
     expected_res = np.array([[1, 3, 2, 4], [9, 11, 10, 12], [5, 7, 6, 8], [13, 15, 14, 16]])
 
-    res = permute_systems(test_input_mat, [2, 1], [2, 2])
+    res = permute_systems(test_input_mat, [1, 0], dim=[2, 2])
 
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
@@ -34,7 +34,7 @@ def test_permute_systems_m2_m2_np_array():
 
     expected_res = np.array([[1, 3, 2, 4], [9, 11, 10, 12], [5, 7, 6, 8], [13, 15, 14, 16]])
 
-    res = permute_systems(test_input_mat, np.array([2, 1]))
+    res = permute_systems(test_input_mat, np.array([1, 0]))
 
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
@@ -68,7 +68,7 @@ def permute_systems_test_2_3_1():
         ]
     )
 
-    res = permute_systems(test_input_mat, [2, 3, 1])
+    res = permute_systems(test_input_mat, [1, 2, 0])
 
     bool_mat = np.isclose(res, expected_res)
     np.testing.assert_equal(np.all(bool_mat), True)
@@ -96,9 +96,8 @@ def test_permute_systems_16_by_16():
             [151, 152, 183, 184, 215, 216, 247, 248, 159, 160, 191, 192, 223, 224, 255, 256],
         ]
     )
-    perm = [2, 3, 1, 4]
+    perm = [1, 2, 0, 3]
     dim = [[2, 2, 2, 2], [2, 2, 2, 2]]
-
     res = permute_systems(rho, perm, dim, True, False)
     expected_res = np.array(
         [
@@ -152,7 +151,7 @@ def test_permute_systems_invalid_perm_vector():
     """Invalid input for permute systems."""
     with np.testing.assert_raises(ValueError):
         test_input_mat = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
-        permute_systems(test_input_mat, [0, 1])
+        permute_systems(test_input_mat, [-1, 0])
 
 
 def test_permute_systems_invalid_empty_input():
diff --git a/toqito/state_opt/optimal_clone.py b/toqito/state_opt/optimal_clone.py
index b9c118060..b086af2df 100644
--- a/toqito/state_opt/optimal_clone.py
+++ b/toqito/state_opt/optimal_clone.py
@@ -130,7 +130,7 @@ def optimal_clone(
         # sequence from: https://oeis.org/A023123
         q_a = tensor(q_a, num_reps)
         perm = []
-        for i in range(1, num_spaces + 1):
+        for i in range(num_spaces ):
             perm.append(i)
             var = i
             for j in range(1, num_reps):
@@ -141,7 +141,6 @@ def optimal_clone(
         return primal_problem(q_a, pperm, num_reps)
     return dual_problem(q_a, pperm, num_reps)
 
-
 def primal_problem(q_a: np.ndarray, pperm: np.ndarray, num_reps: int) -> float:
     """Primal problem for counterfeit attack.
 
diff --git a/toqito/state_props/is_product.py b/toqito/state_props/is_product.py
index 15ffb5146..9ba1775ec 100644
--- a/toqito/state_props/is_product.py
+++ b/toqito/state_props/is_product.py
@@ -132,7 +132,7 @@ def _operator_is_product(rho: np.ndarray, dim: int | list[int] = None) -> list[i
         dim = np.array([dim, dim])
 
     op_1 = rho.reshape(int(np.prod(np.prod(dim))), 1)
-    perm = swap(np.array(list(range(2 * num_sys))), [1, 2], [2, num_sys]) + 1
+    perm = swap(np.array(list(range(2 * num_sys))), [1, 2], [2, num_sys])
     perm_dim = np.concatenate((dim[1, :].astype(int), dim[0, :].astype(int)))
     op_3 = permute_systems(op_1, perm, perm_dim).reshape(-1, 1)
 
diff --git a/toqito/states/werner.py b/toqito/states/werner.py
index 6dab7bd1a..f7c7bfda8 100644
--- a/toqito/states/werner.py
+++ b/toqito/states/werner.py
@@ -106,7 +106,7 @@ def werner(dim: int, alpha: float | list[float]) -> np.ndarray:
         # Done error checking and computing the number of parties
         # -- now compute the Werner state.
         perms = list(itertools.permutations(range(n_var)))
-        sorted_perms = np.argsort(perms, axis=1) + 1
+        sorted_perms = np.argsort(perms, axis=1)
 
         rho = np.identity(dim**n_var)
         for i in range(2, n_fac):