toqito.states.brauer
====================

.. py:module:: toqito.states.brauer

.. autoapi-nested-parse::

   Brauer states are the p_val-fold tensor product of the standard maximally-entangled pure states.





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

.. py:function:: brauer(dim, p_val)

   Produce all Brauer states [@WikiBrauer].

   Produce a matrix whose columns are all of the (unnormalized) "Brauer" states: states that are the `p_val`-fold
   tensor product of the standard maximally-entangled pure state on `dim` local dimensions. There are many such
   states, since there are many different ways to group the `2 * p_val` parties into `p_val` pairs (with
   each pair corresponding to one maximally-entangled state).

   The exact number of such states is:

   ```python exec="1" source="above"
   import math
   import numpy as np
   p_val = 2
   print(math.factorial(2 * p_val) / (math.factorial(p_val) * 2**p_val))
   ```

   which is the number of columns of the returned matrix.

   This function has been adapted from QETLAB.

   .. rubric:: Examples

   Generate a matrix whose columns are all Brauer states on 4 qubits.

   ```python exec="1" source="above"
   from toqito.states import brauer
   print(brauer(2, 2))
   ```

   :param dim: Dimension of each local subsystem
   :param p_val: Half of the number of parties (i.e., the state that this function computes will live in
   :param \:
   :type \: (\mathbb{C}^D)^{\otimes 2 P})\

   :returns: Matrix whose columns are all of the unnormalized Brauer states.