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

.. py:module:: toqito.state_props.is_ensemble

.. autoapi-nested-parse::

   Checks if a set of quantum states form an 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 [@Watrous_2018_TQI].

   An ensemble of quantum states is defined by a function

   \[
       \eta : \Gamma \rightarrow \text{Pos}(\mathcal{X})
   \]

   that satisfies

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

   .. rubric:: Examples

   Consider the following set of matrices

   \[
       \eta = \left\{ \rho_0, \rho_1 \right\}
   \]

   where

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

   The set \(\eta\) constitutes a valid ensemble.

   ```python exec="1" source="above"
   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]
   print(is_ensemble(states))
   ```

   :param states: The list of states to check.

   :returns: `True` if states form an ensemble and `False` otherwise.