toqito.states.bb84
==================

.. py:module:: toqito.states.bb84

.. autoapi-nested-parse::

   BB84 states represent the BB84 basis states, which are based on BB84, a quantum key distribution scheme.

   In the BB884 scheme, each qubit is encoded with one of the 4 polarization states: 0, 1, +45° or -45°.





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

.. py:function:: bb84()

   Obtain the BB84 basis states [@WikiBB84].

   The BB84 basis states are defined as

   \[
       |0\rangle := \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \quad \\
       |1\rangle := \begin{pmatrix} 0 \\ 1 \end{pmatrix}, \quad \\
       |+\rangle := \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ 1 \end{pmatrix}, \quad \\
       |-\rangle := \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ -1 \end{pmatrix}.
   \]

   .. rubric:: Examples

   The BB84 basis states can be obtained in `|toqito⟩` as follows in the form of a list of
   arrays.

   ```python exec="1" source="above"
   from toqito.states import bb84
   print(bb84())
   ```

   :returns: The four BB84 basis states.