:py:mod:`state_ops.pure_to_mixed`
=================================

.. py:module:: state_ops.pure_to_mixed

.. autoapi-nested-parse::

   Pure to mixed operation.



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


Functions
~~~~~~~~~

.. autoapisummary::

   state_ops.pure_to_mixed.pure_to_mixed



.. py:function:: pure_to_mixed(phi)

   Convert a state vector or density matrix to a density matrix.

   .. rubric:: Examples

   It is possible to convert a pure state vector to a mixed state vector using the :code:`toqito`
   package. Consider the following Bell state

   .. math::
       u = \frac{1}{\sqrt{2}} \left( |00 \rangle + |11 \rangle \right).

   The corresponding mixed state from :math:`u` is calculated as

   .. math::
       \rho = u u^* = \frac{1}{2} \begin{pmatrix}
                                       1 & 0 & 0 & 1 \\
                                       0 & 0 & 0 & 0 \\
                                       0 & 0 & 0 & 0 \\
                                       1 & 0 & 0 & 1
                                  \end{pmatrix}

   Using :code:`toqito`, we can obtain this matrix as follows.

   >>> from toqito.states import bell
   >>> from toqito.state_ops import pure_to_mixed
   >>> phi = bell(0)
   >>> pure_to_mixed(phi)
   array([[0.5, 0. , 0. , 0.5],
          [0. , 0. , 0. , 0. ],
          [0. , 0. , 0. , 0. ],
          [0.5, 0. , 0. , 0.5]])

   We can also give matrix inputs to the function in :code:`toqito`.

   >>> from toqito.states import bell
   >>> from toqito.state_ops import pure_to_mixed
   >>> phi = bell(0) * bell(0).conj().T
   >>> pure_to_mixed(phi)
   array([[0.5, 0. , 0. , 0.5],
          [0. , 0. , 0. , 0. ],
          [0. , 0. , 0. , 0. ],
          [0.5, 0. , 0. , 0.5]])

   :raises ValueError: If matrix is not square.
   :param phi: A density matrix or a pure state vector.
   :return: density matrix representation of :code:`phi`, regardless of whether :code:`phi` is
            itself already a density matrix or if if is a pure state vector.