:py:mod:`state_props.is_mixed`
==============================

.. py:module:: state_props.is_mixed

.. autoapi-nested-parse::

   Check if state is mixed.



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


Functions
~~~~~~~~~

.. autoapisummary::

   state_props.is_mixed.is_mixed



.. py:function:: is_mixed(state)

   Determine if a given quantum state is mixed :cite:`WikiMixedSt`.

   A mixed state by definition is a state that is not pure.

   .. rubric:: Examples

   Consider the following density matrix:

   .. math::
       \rho =  \begin{pmatrix}
                   \frac{3}{4} & 0 \\
                   0 & \frac{1}{4}
               \end{pmatrix} \in \text{D}(\mathcal{X}).

   Calculating the rank of :math:`\rho` yields that the :math:`\rho` is a mixed state. This can be
   confirmed in :code:`toqito` as follows:

   >>> from toqito.states import basis
   >>> from toqito.state_props import is_mixed
   >>> e_0, e_1 = basis(2, 0), basis(2, 1)
   >>> rho = 3 / 4 * e_0 * e_0.conj().T + 1 / 4 * e_1 * e_1.conj().T
   >>> is_mixed(rho)
   True

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param state: The density matrix representing the quantum state.
   :return: :code:`True` if state is mixed and :code:`False` otherwise.