Remove basis function in favor of standard_basis

docs/intro_tutorial.rst

@@ -44,14 +44,15 @@ can be defined in :code:`toqito` as such
 
 .. code-block:: python
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
+    >>> e_0, e_1 = standard_basis(2)
     >>> # |0>
-    >>> basis(2, 0)
+    >>> e_0
     array([[1],
            [0]])
 
     >>> # |1>
-    >>> basis(2, 1)
+    >>> e_1
     array([[0],
            [1]])
 
@@ -66,7 +67,8 @@ using :code:`toqito` as
 .. code-block:: python
 
     >>> import numpy as np
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> from toqito.matrices import standard_basis
+    >>> e_0, e_1 = standard_basis(2)
     >>> u_0 = 1/np.sqrt(2) * (np.kron(e_0, e_0) + np.kron(e_1, e_1))
     >>> u_0
     array([[0.70710678],
@@ -91,7 +93,8 @@ In :code:`toqito`, that can be obtained as
 .. code-block:: python
 
     >>> import numpy as np
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> from toqito.matrices import standard_basis
+    >>> e_0, e_1 = standard_basis(2)
     >>> u_0 = 1/np.sqrt(2) * (np.kron(e_0, e_0) + np.kron(e_1, e_1))
     >>> rho_0 = u_0 @ u_0.conj().T
     >>> rho_0

docs/tutorials.extended_nonlocal_games.rst

@@ -271,10 +271,10 @@ arrays where :code:`prob_mat` corresponds to the probability distribution
 
     >>> # Define the BB84 extended nonlocal game.
     >>> import numpy as np
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>>
     >>> # The basis: {|0>, |1>}:
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis
     >>>
     >>> # The basis: {|+>, |->}:
     >>> e_p = (e_0 + e_1) / np.sqrt(2)

docs/tutorials.state_distinguishability.rst

@@ -115,11 +115,11 @@ Using :code:`toqito`, we can calculate this probability directly as follows:
 .. code-block:: python
 
     >>> import numpy as np
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.state_opt import state_distinguishability
     >>> 
     >>> # Define the standard basis |0> and |1>
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>>
     >>> # Define the corresponding density matrices of |0> and |1> 
     >>> # given as |0><0| and |1><1|, respectively.

toqito/channel_metrics/fidelity_of_separability.py

@@ -84,8 +84,9 @@ def fidelity_of_separability(
     >>> import numpy as np
     >>> from toqito.state_metrics import fidelity_of_separability
     >>> from toqito.matrix_ops import tensor
-    >>> from toqito.states import basis
-    >>> state = tensor(basis(2, 0), basis(2, 0))
+    >>> from toqito.matrices import standard_basis
+    >>> e_0, e_1 = standard_basis(2)
+    >>> state = tensor(e_0, e_1)
     >>> rho = state @ state.conj().T
     >>> np.around(fidelity_of_separability(rho, [2, 2]), decimals=2)
     np.float64(1.0)

toqito/matrix_ops/tensor.py

@@ -52,9 +52,9 @@ def tensor(*args) -> np.ndarray:
 
     This can be accomplished in :code:`toqito` as follows.
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.matrix_ops import tensor
-    >>> e_0 = basis(2, 0)
+    >>> e_0, _ = standard_basis(2)
     >>> tensor(e_0, e_0)
     array([[1],
            [0],
@@ -71,9 +71,9 @@ def tensor(*args) -> np.ndarray:
 
     in :code:`toqito` as follows.
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.matrix_ops import tensor
-    >>> e_0 = basis(2, 0)
+    >>> e_0, _ = standard_basis(2)
     >>> tensor(e_0, 3)
     array([[1],
            [0],
@@ -91,9 +91,9 @@ def tensor(*args) -> np.ndarray:
     compute :math:`e_0 \otimes e_1 \otimes e_0`, we can do
     so as follows.
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.matrix_ops import tensor
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>> tensor([e_0, e_1, e_0])
     array([[0],
            [0],

toqito/matrix_ops/tests/test_tensor.py

@@ -3,10 +3,10 @@
 import numpy as np
 import pytest
 
+from toqito.matrices import standard_basis
 from toqito.matrix_ops import tensor
-from toqito.states import basis
 
-e_0, e_1 = basis(2, 0), basis(2, 1)
+e_0, e_1 = standard_basis(2)
 matrix1 = np.array([[1, 2]])
 matrix2 = np.array([[3], [4]])
 matrix3 = np.array([[5, 6]])

toqito/matrix_ops/tests/test_tensor_comb.py

@@ -3,10 +3,10 @@
 import numpy as np
 import pytest
 
+from toqito.matrices import standard_basis
 from toqito.matrix_ops import tensor_comb
-from toqito.states import basis
 
-e_0, e_1 = basis(2, 0), basis(2, 1)
+e_0, e_1 = standard_basis(2)
 
 
 @pytest.mark.parametrize(

toqito/matrix_props/tests/test_sk_norm.py

@@ -3,8 +3,9 @@
 import numpy as np
 import pytest
 
+from toqito.matrices import standard_basis
 from toqito.matrix_props import sk_operator_norm
-from toqito.states import basis, max_entangled, werner
+from toqito.states import max_entangled, werner
 
 
 def test_s1_norm_example():
@@ -60,10 +61,8 @@ def test_s1_norm_werner(n, a):
 
 def test_sk_norm_hermitian_not_psd():
     """Test S(k) norm of a Hermitian but not PSD matrix."""
-    e_0 = basis(2, 0)
+    e_0, e_1 = standard_basis(2)
     e_00 = np.kron(e_0, e_0)
-
-    e_1 = basis(2, 1)
     e_11 = np.kron(e_1, e_1)
 
     mat = e_00 @ e_11.T + e_11 @ e_00.T

toqito/matrix_props/tests/test_trace_norm.py

@@ -2,13 +2,13 @@
 
 import numpy as np
 
+from toqito.matrices import standard_basis
 from toqito.matrix_props import trace_norm
-from toqito.states import basis
 
 
 def test_trace_norm():
     """Test trace norm."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     e_00 = np.kron(e_0, e_0)
     e_11 = np.kron(e_1, e_1)
 

toqito/measurement_ops/measure.py

@@ -34,10 +34,10 @@ def measure(measurement: np.ndarray, state: np.ndarray) -> float:
     .. math::
         P_0 = e_0 e_0^* \quad \text{and} \quad P_1 = e_1 e_1^*.
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basi
     >>> from toqito.measurement_ops import measure
     >>> import numpy as np
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>>
     >>> u = 1/np.sqrt(3) * e_0 + np.sqrt(2/3) * e_1
     >>> rho = u @ u.conj().T

toqito/measurement_ops/tests/test_measure.py

@@ -2,13 +2,13 @@
 
 import numpy as np
 
+from toqito.matrices import standard_basis
 from toqito.measurement_ops import measure
-from toqito.states import basis
 
 
 def test_measure_state():
     """Test measure on quantum state."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     psi = 1 / np.sqrt(3) * e_0 + np.sqrt(2 / 3) * e_1
     rho = psi @ psi.conj().T
 

toqito/nonlocal_games/quantum_hedging.py

@@ -33,10 +33,10 @@ class QuantumHedging:
 
     >>> import numpy as np
     >>> from numpy import kron, cos, sin, pi, sqrt, isclose
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.nonlocal_games.quantum_hedging import QuantumHedging
     >>>
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>> e_00, e_01 = kron(e_0, e_0), kron(e_0, e_1)
     >>> e_10, e_11 = kron(e_1, e_0), kron(e_1, e_1)
     >>>

toqito/nonlocal_games/tests/test_extended_nonlocal_game.py

@@ -4,8 +4,8 @@
 
 import numpy as np
 
+from toqito.matrices import standard_basis
 from toqito.nonlocal_games.extended_nonlocal_game import ExtendedNonlocalGame
-from toqito.states import basis
 
 
 class TestExtendedNonlocalGame(unittest.TestCase):
@@ -14,7 +14,7 @@ class TestExtendedNonlocalGame(unittest.TestCase):
     @staticmethod
     def bb84_extended_nonlocal_game():
         """Define the BB84 extended nonlocal game."""
-        e_0, e_1 = basis(2, 0), basis(2, 1)
+        e_0, e_1 = standard_basis(2)
         e_p = (e_0 + e_1) / np.sqrt(2)
         e_m = (e_0 - e_1) / np.sqrt(2)
 
@@ -61,7 +61,7 @@ def moe_mub_4_in_3_out_game():
         prob_mat = 1 / 4 * np.identity(4)
 
         dim = 3
-        e_0, e_1, e_2 = basis(dim, 0), basis(dim, 1), basis(dim, 2)
+        e_0, e_1, e_2 = standard_basis(3)
 
         eta = np.exp((2 * np.pi * 1j) / dim)
         mub_0 = [e_0, e_1, e_2]

toqito/nonlocal_games/tests/test_quantum_hedging.py

@@ -4,14 +4,14 @@
 
 from numpy import cos, isclose, kron, pi, sin, sqrt
 
+from toqito.matrices import standard_basis
 from toqito.nonlocal_games.quantum_hedging import QuantumHedging
-from toqito.states import basis
 
 
 class TestQuantumHedging(unittest.TestCase):
     """Unit test for hedging_value."""
 
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     e_00, e_01 = kron(e_0, e_0), kron(e_0, e_1)
     e_10, e_11 = kron(e_1, e_0), kron(e_1, e_1)
 

toqito/state_metrics/fidelity_of_separability.py

@@ -91,8 +91,9 @@ def fidelity_of_separability(
     >>> import numpy as np
     >>> from toqito.state_metrics import fidelity_of_separability
     >>> from toqito.matrix_ops import tensor
-    >>> from toqito.states import basis
-    >>> state = tensor(basis(2, 0), basis(2, 0))
+    >>> from toqito.matrices import standard_basis
+    >>> e_0, e_1 = standard_basis(2)
+    >>> state = tensor(e_0, e_1)
     >>> rho = state @ state.conj().T
     >>> np.around(fidelity_of_separability(rho, [2, 2]), decimals=2)
     np.float64(1.0)

toqito/state_metrics/helstrom_holevo.py

@@ -34,10 +34,10 @@ def helstrom_holevo(rho: np.ndarray, sigma: np.ndarray) -> float:
     Calculating the Helstrom-Holevo distance of states that are identical yield a value of
     :math:`1/2`. This can be verified in :code:`toqito` as follows.
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.state_metrics import helstrom_holevo
     >>> import numpy as np
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>> e_00 = np.kron(e_0, e_0)
     >>> e_11 = np.kron(e_1, e_1)
     >>>

toqito/state_metrics/sub_fidelity.py

@@ -35,9 +35,9 @@ def sub_fidelity(rho: np.ndarray, sigma: np.ndarray) -> float:
     Calculating the fidelity between the states :math:`\rho` and :math:`\sigma` as :math:`F(\rho, \sigma) \approx
     0.774`. This can be observed in :code:`toqito` as
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.state_metrics import fidelity
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>> rho = 3 / 4 * e_0 @ e_0.conj().T + 1 / 4 * e_1 @ e_1.conj().T
     >>> sigma = 1/8 * e_0 @ e_0.conj().T + 7/8 * e_1 @ e_1.conj().T
     >>> fidelity(rho, sigma)
@@ -46,9 +46,9 @@ def sub_fidelity(rho: np.ndarray, sigma: np.ndarray) -> float:
     As the sub-fidelity is a lower bound on the fidelity, that is :math:`E(\rho, \sigma) \leq F(\rho, \sigma)`, we can
     use :code:`toqito` to observe that :math:`E(\rho, \sigma) \approx 0.599\leq F(\rho, \sigma \approx 0.774`.
 
-    >>> from toqito.states import basis
+    >>> from toqito.matrices import standard_basis
     >>> from toqito.state_metrics import sub_fidelity
-    >>> e_0, e_1 = basis(2, 0), basis(2, 1)
+    >>> e_0, e_1 = standard_basis(2)
     >>> rho = 3 / 4 * e_0 @ e_0.conj().T + 1 / 4 * e_1 @ e_1.conj().T
     >>> sigma = 1/8 * e_0 @ e_0.conj().T + 7/8 * e_1 @ e_1.conj().T
     >>> sub_fidelity(rho, sigma)

toqito/state_metrics/tests/test_bures_angle.py

@@ -2,8 +2,8 @@
 
 import numpy as np
 
+from toqito.matrices import standard_basis
 from toqito.state_metrics import bures_angle
-from toqito.states import basis
 
 
 def test_bures_angle_default():
@@ -17,7 +17,7 @@ def test_bures_angle_default():
 
 def test_bures_angle_non_identical_states_1():
     """Test the bures_angle between two non-identical states."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     rho = 3 / 4 * e_0 @ e_0.conj().T + 1 / 4 * e_1 @ e_1.conj().T
     sigma = 2 / 3 * e_0 @ e_0.conj().T + 1 / 3 * e_1 @ e_1.conj().T
 
@@ -27,7 +27,7 @@ def test_bures_angle_non_identical_states_1():
 
 def test_bures_angle_non_identical_states_2():
     """Test the bures_angle between two non-identical states."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     rho = 3 / 4 * e_0 @ e_0.conj().T + 1 / 4 * e_1 @ e_1.conj().T
     sigma = 1 / 8 * e_0 @ e_0.conj().T + 7 / 8 * e_1 @ e_1.conj().T
 
@@ -37,7 +37,7 @@ def test_bures_angle_non_identical_states_2():
 
 def test_bures_angle_pure_states():
     """Test the bures_angle between two pure states."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     e_plus = (e_0 + e_1) / np.sqrt(2)
     rho = e_plus @ e_plus.conj().T
     sigma = e_0 @ e_0.conj().T

toqito/state_metrics/tests/test_bures_distance.py

@@ -2,8 +2,8 @@
 
 import numpy as np
 
+from toqito.matrices import standard_basis
 from toqito.state_metrics import bures_distance
-from toqito.states import basis
 
 
 def test_bures_distance_default():
@@ -17,23 +17,23 @@ def test_bures_distance_default():
 
 def test_bures_distance_non_identical_states_1():
     """Test the bures_distance between two non-identical states."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     rho = 3 / 4 * e_0 @ e_0.conj().T + 1 / 4 * e_1 @ e_1.conj().T
     sigma = 2 / 3 * e_0 @ e_0.conj().T + 1 / 3 * e_1 @ e_1.conj().T
     np.testing.assert_equal(np.isclose(bures_distance(rho, sigma), 0.0918, rtol=1e-03), True)
 
 
 def test_bures_distance_non_identical_states_2():
     """Test the bures_distance between two non-identical states."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     rho = 3 / 4 * e_0 @ e_0.conj().T + 1 / 4 * e_1 @ e_1.conj().T
     sigma = 1 / 8 * e_0 @ e_0.conj().T + 7 / 8 * e_1 @ e_1.conj().T
     np.testing.assert_equal(np.isclose(bures_distance(rho, sigma), 0.6724, rtol=1e-03), True)
 
 
 def test_bures_distance_pure_states():
     """Test the bures_distance between two pure states."""
-    e_0, e_1 = basis(2, 0), basis(2, 1)
+    e_0, e_1 = standard_basis(2)
     e_plus = (e_0 + e_1) / np.sqrt(2)
     rho = e_plus @ e_plus.conj().T
     sigma = e_0 @ e_0.conj().T