state_props.is_ensemble
=======================

.. py:module:: state_props.is_ensemble

.. autoapi-nested-parse::

   Checks if a set of quantum states form an ensemble.



Functions
---------

.. autoapisummary::

   state_props.is_ensemble.is_ensemble


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

.. py:function:: is_ensemble(states)

   Determine if a set of states constitute an ensemble.

   For more info, see Section: Ensemble Of Quantum States from cite:`Watrous_2018_TQI`.

   An ensemble of quantum states is defined by a function

   .. math::
       \eta : \Gamma \rightarrow \text{Pos}(\mathcal{X})

   that satisfies

   .. math::
       \text{Tr}\left( \sum_{a \in \Gamma} \eta(a) \right) = 1.

   .. rubric:: Examples

   Consider the following set of matrices

   .. math::
       \eta = \left\{ \rho_0, \rho_1 \right\}

   where

   .. math::
       \rho_0 = \frac{1}{2} \begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}, \quad
       \rho_1 = \frac{1}{2} \begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}.

   The set :math:`\eta` constitutes a valid ensemble.

   .. jupyter-execute::

       from toqito.state_props import is_ensemble
       import numpy as np
       rho_0 = np.array([[0.5, 0], [0, 0]])
       rho_1 = np.array([[0, 0], [0, 0.5]])
       states = [rho_0, rho_1]
       is_ensemble(states)

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param states: The list of states to check.
   :return: :code:`True` if states form an ensemble and :code:`False` otherwise.