Merge pull request #327 from vprusso/bb84-states

Adding BB84 states.

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",

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

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]]

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)