:py:mod:`states.chessboard`
===========================

.. py:module:: states.chessboard

.. autoapi-nested-parse::

   Chessboard state.



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


Functions
~~~~~~~~~

.. autoapisummary::

   states.chessboard.chessboard



.. py:function:: chessboard(mat_params, s_param = None, t_param = None)

   Produce a chessboard state :cite:`Dur_2000_ThreeQubits`.

   Generates the chessboard state defined in :cite:`Dur_2000_ThreeQubits`. Note that, for certain choices of
   :code:`s_param` and :code:`t_param`, this state will not have positive partial transpose, and
   thus may not be bound entangled.

   .. rubric:: Examples

   The standard chessboard state can be invoked using :code:`toqito` as

   >>> from toqito.states import chessboard
   >>> chessboard([1, 2, 3, 4, 5, 6], 7, 8)
   array([[ 0.22592593,  0.        ,  0.12962963,  0.        ,  0.        ,
            0.        ,  0.17777778,  0.        ,  0.        ],
          [ 0.        ,  0.01851852,  0.        ,  0.        ,  0.        ,
            0.01111111,  0.        ,  0.02962963,  0.        ],
          [ 0.12962963,  0.        ,  0.18148148,  0.        ,  0.15555556,
            0.        ,  0.        ,  0.        ,  0.        ],
          [ 0.        ,  0.        ,  0.        ,  0.01851852,  0.        ,
            0.02222222,  0.        , -0.01481481,  0.        ],
          [ 0.        ,  0.        ,  0.15555556,  0.        ,  0.22592593,
            0.        , -0.14814815,  0.        ,  0.        ],
          [ 0.        ,  0.01111111,  0.        ,  0.02222222,  0.        ,
            0.03333333,  0.        ,  0.        ,  0.        ],
          [ 0.17777778,  0.        ,  0.        ,  0.        , -0.14814815,
            0.        ,  0.23703704,  0.        ,  0.        ],
          [ 0.        ,  0.02962963,  0.        , -0.01481481,  0.        ,
            0.        ,  0.        ,  0.05925926,  0.        ],
          [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
            0.        ,  0.        ,  0.        ,  0.        ]])

   .. rubric:: References

   .. bibliography::
     :filter: docname in docnames

   :param mat_params: Parameters of the chessboard state as defined in :cite:`Dur_2000_ThreeQubits`.
   :param s_param: Default is :code:`np.conj(mat_params[2]) / np.conj(mat_params[5])`.
   :param t_param: Default is :code:`t_param = mat_params[0] * mat_params[3] / mat_params[4]`.
   :return: A chessboard state.