toqito.state_props.is_mixed
===========================

.. py:module:: toqito.state_props.is_mixed

.. autoapi-nested-parse::

   Checks if a quantum state is mixed.





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

.. py:function:: is_mixed(state)

   Determine if a given quantum state is mixed [@WikiMixedSt].

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

   .. rubric:: Examples

   Consider the following density matrix:

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

   Calculating the rank of \(\rho\) yields that the \(\rho\) is a mixed state. This can be
   confirmed in `|toqito⟩` as follows:

   ```python exec="1" source="above"
   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
   print(is_mixed(rho))
   ```

   :param state: The density matrix representing the quantum state.

   :returns: `True` if state is mixed and `False` otherwise.