toqito.random.random_povm(dim: int, num_inputs: int, num_outputs: int) → numpy.ndarray[source]

Generate random positive operator valued measurements (POVMs) [WIKPOVM].


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 \(2\)-by-\(2\) POVMs of dimension with \(2\) inputs and \(2\) outputs.

>>> from toqito.random 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]]


[WIKPOVM]Wikipedia: POVM
  • dim – The dimensions of the measurements.
  • num_inputs – The number of inputs for the measurement.
  • num_outputs – The number of outputs for the measurement.

A set of dim-by-dim POVMs of shape (dim, dim, num_inputs, num_outputs).