:py:mod:`rand.random_povm`
==========================

.. py:module:: rand.random_povm

.. autoapi-nested-parse::

   Generate random POVM.



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


Functions
~~~~~~~~~

.. autoapisummary::

   rand.random_povm.random_povm



.. py:function:: random_povm(dim, num_inputs, num_outputs)

   Generate random positive operator valued measurements (POVMs) :cite:`WikiPOVM`.

   .. rubric:: Examples

   We can generate a set of `dim`-by-`dim` POVMs consisting of a specific dimension along with a given number of
   measurement inputs and measurement outputs. As an example, we can construct a random set of :math:`2`-by-:math:`2`
   POVMs of dimension with :math:`2` inputs and :math:`2` outputs.

   >>> from toqito.rand import random_povm
   >>> import numpy as np
   >>>
   >>> dim, num_inputs, num_outputs = 2, 2, 2
   >>> povms = random_povm(dim, num_inputs, num_outputs)
   >>> povms
   [[[[ 0.40313832+0.j,  0.59686168+0.j],
      [ 0.91134633+0.j,  0.08865367+0.j]],
    [[-0.27285707+0.j,  0.27285707+0.j],
     [-0.12086852+0.j,  0.12086852+0.j]]],
    [[[-0.27285707+0.j,  0.27285707+0.j],
     [-0.12086852+0.j,  0.12086852+0.j]],
    [[ 0.452533  +0.j,  0.547467  +0.j],
     [ 0.34692158+0.j,  0.65307842+0.j]]]]

   We can verify that this constitutes a valid set of POVM elements as checking that these operators all sum to the
   identity operator.

   >>> np.round(povms[:, :, 0, 0] + povms[:, :, 0, 1])
   [[1.+0.j, 0.+0.j],
    [0.+0.j, 1.+0.j]]

   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

   :param dim: The dimensions of the measurements.
   :param num_inputs: The number of inputs for the measurement.
   :param num_outputs: The number of outputs for the measurement.
   :return: A set of `dim`-by-`dim` POVMs of shape `(dim, dim, num_inputs, num_outputs)`.