From 7ad05e76fe0158b412d3a3c3718e92fb82331daa Mon Sep 17 00:00:00 2001
From: vrusso <vincentrusso1@gmail.com>
Date: Sun, 3 Dec 2023 21:47:49 -0500
Subject: [PATCH 1/4] Adding BB84 states.

---
 docs/articles.bib                |  8 ++++++
 toqito/states/bb84.py            | 43 ++++++++++++++++++++++++++++++++
 toqito/states/tests/test_bb84.py | 17 +++++++++++++
 3 files changed, 68 insertions(+)
 create mode 100644 toqito/states/bb84.py
 create mode 100644 toqito/states/tests/test_bb84.py

diff --git a/docs/articles.bib b/docs/articles.bib
index 42def0879..9f507dd74 100644
--- a/docs/articles.bib
+++ b/docs/articles.bib
@@ -745,6 +745,14 @@ @misc{WikiAsymmOp
   
 }
 
+@misc{WikiBB84,
+  author  = "Wikipedia",
+  title   = "BB84",
+  howpublished = {https://en.wikipedia.org/wiki/BB84}
+  
+}
+
+
 @misc{WikiBellSt,
   author  = "Wikipedia",
   title   = "Bell State",
diff --git a/toqito/states/bb84.py b/toqito/states/bb84.py
new file mode 100644
index 000000000..9962479e6
--- /dev/null
+++ b/toqito/states/bb84.py
@@ -0,0 +1,43 @@
+"""BB84 basis states"""
+import numpy as np
+from toqito.matrices import standard_basis
+
+
+def bb84() -> np.ndarray:
+    r"""Obtain the BB84 basis states :cite:`WikiBB84`.
+
+    The BB84 basis states are defined as
+
+    .. math::
+        |0\rangle := \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \quad \\
+        |1\rangle := \begin{pmatrix} 0 \\ 1 \end{pmatrix}, \quad \\
+        |+\rangle := \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ 1 \end{pmatrix}, \quad \\
+        |-\rangle := \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ -1 \end{pmatrix}.
+
+    Examples
+    ==========
+    The BB84 basis states can be obtained in :code:`toqito` as follows.
+
+    >>> from toqito.states import bb84
+    >>> states = bb84()
+    >>> print(f"|0> = {x[0][0].T}, \n |1> = {x[0][1].T}")
+    >>> print(f"|+> = {x[1][0].T}, \n |-> = {x[1][1].T}")
+    |0> = [[1. 0.]], 
+    |1> = [[0. 1.]]
+    |+> = [[0.70710678 0.70710678]], 
+    |-> = [[ 0.70710678 -0.70710678]]    
+
+    References
+    ==========
+    .. bibliography::
+        :filter: docname in docnames
+
+
+    :return: The four BB84 basis states.
+    """
+    # Computational basis states |0>, |1>:
+    e_0, e_1 = standard_basis(2)
+    # Plus/minus basis |+>, |->
+    e_p, e_m = (e_0 + e_1) / np.sqrt(2), (e_0 - e_1) / np.sqrt(2)
+    return [[e_0, e_1], [e_p, e_m]]
+    
\ No newline at end of file
diff --git a/toqito/states/tests/test_bb84.py b/toqito/states/tests/test_bb84.py
new file mode 100644
index 000000000..70b472638
--- /dev/null
+++ b/toqito/states/tests/test_bb84.py
@@ -0,0 +1,17 @@
+"""Test BB84."""
+import numpy as np
+
+from toqito.states import bb84
+
+
+def test_bb84():
+    """Test function generates the correct BB84 states."""
+    e_0, e_1 = np.array([[1], [0]]), np.array([[0], [1]])
+    e_p, e_m = (e_0 + e_1) / np.sqrt(2), (e_0 - e_1) / np.sqrt(2)
+
+    states = bb84()
+
+    np.testing.assert_array_equal(states[0][0], e_0)
+    np.testing.assert_array_equal(states[0][1], e_1)
+    np.testing.assert_array_equal(states[1][0], e_p)
+    np.testing.assert_array_equal(states[1][1], e_m)

From ff0329a492828b7e8186d99280894dad390067d0 Mon Sep 17 00:00:00 2001
From: vrusso <vincentrusso1@gmail.com>
Date: Sun, 3 Dec 2023 21:55:37 -0500
Subject: [PATCH 2/4] Fixing failing test.

---
 toqito/states/__init__.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/toqito/states/__init__.py b/toqito/states/__init__.py
index e8d018aab..c6614dffd 100644
--- a/toqito/states/__init__.py
+++ b/toqito/states/__init__.py
@@ -1,5 +1,6 @@
 """Quantum states."""
 from toqito.states.basis import basis
+from toqito.states.bb84 import bb84
 from toqito.states.bell import bell
 from toqito.states.chessboard import chessboard
 from toqito.states.domino import domino

From 9bec85b9848dec86cd68a2eb302a1a6434e309f9 Mon Sep 17 00:00:00 2001
From: vrusso <vincentrusso1@gmail.com>
Date: Sun, 3 Dec 2023 22:17:04 -0500
Subject: [PATCH 3/4] fixing failing test.

---
 toqito/states/bb84.py | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/toqito/states/bb84.py b/toqito/states/bb84.py
index 9962479e6..3518611da 100644
--- a/toqito/states/bb84.py
+++ b/toqito/states/bb84.py
@@ -1,4 +1,4 @@
-"""BB84 basis states"""
+"""BB84 basis states."""
 import numpy as np
 from toqito.matrices import standard_basis
 
@@ -22,10 +22,10 @@ def bb84() -> np.ndarray:
     >>> states = bb84()
     >>> print(f"|0> = {x[0][0].T}, \n |1> = {x[0][1].T}")
     >>> print(f"|+> = {x[1][0].T}, \n |-> = {x[1][1].T}")
-    |0> = [[1. 0.]], 
+    |0> = [[1. 0.]],
     |1> = [[0. 1.]]
-    |+> = [[0.70710678 0.70710678]], 
-    |-> = [[ 0.70710678 -0.70710678]]    
+    |+> = [[0.70710678 0.70710678]],
+    |-> = [[ 0.70710678 -0.70710678]]
 
     References
     ==========
@@ -40,4 +40,3 @@ def bb84() -> np.ndarray:
     # Plus/minus basis |+>, |->
     e_p, e_m = (e_0 + e_1) / np.sqrt(2), (e_0 - e_1) / np.sqrt(2)
     return [[e_0, e_1], [e_p, e_m]]
-    
\ No newline at end of file

From be349bb1927b44bfade0a835f7d231a6da6b47f4 Mon Sep 17 00:00:00 2001
From: vrusso <vincentrusso1@gmail.com>
Date: Sun, 3 Dec 2023 22:31:21 -0500
Subject: [PATCH 4/4] fixing failing test.

---
 toqito/states/bb84.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/toqito/states/bb84.py b/toqito/states/bb84.py
index 3518611da..40ab38172 100644
--- a/toqito/states/bb84.py
+++ b/toqito/states/bb84.py
@@ -1,5 +1,6 @@
 """BB84 basis states."""
 import numpy as np
+
 from toqito.matrices import standard_basis