rand.random_povm
================

.. py:module:: rand.random_povm

.. autoapi-nested-parse::

   Generates a random POVM.



Functions
---------

.. autoapisummary::

   rand.random_povm.random_povm


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

.. py:function:: random_povm(dim, num_inputs, num_outputs, seed = None)

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

   .. jupyter-execute::

    import numpy as np
    from toqito.rand import random_povm

    dim, num_inputs, num_outputs = 2, 2, 2

    povms = random_povm(dim, num_inputs, num_outputs)

    povms

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

   .. jupyter-execute::

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

   It is also possible to add a seed for reproducibility.

   .. jupyter-execute::

    import numpy as np
    from toqito.rand import random_povm

    dim, num_inputs, num_outputs = 2, 2, 2

    povms = random_povm(dim, num_inputs, num_outputs, seed=42)

    povms

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

   .. jupyter-execute:

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

   .. rubric:: References

   .. footbibliography::

   :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.
   :param seed: A seed used to instantiate numpy's random number generator.
   :return: A set of `dim`-by-`dim` POVMs of shape `(dim, dim, num_inputs, num_outputs)`.