:py:mod:`states.bb84`
=====================

.. py:module:: states.bb84

.. autoapi-nested-parse::

   BB84 basis states.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   states.bb84.bb84



.. py:function:: bb84()

   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}.

   .. rubric:: Examples

   The BB84 basis states can be obtained in :code:`toqito` as follows.

   >>> from toqito.states import bb84
   >>> x = 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]]

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :return: The four BB84 basis states.