rand.random_povm
Generate random POVM.
Module Contents
Functions
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Generate random positive operator valued measurements (POVMs) [1]. |
- rand.random_povm.random_povm(dim, num_inputs, num_outputs)
Generate random positive operator valued measurements (POVMs) [1].
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 \(2\)-by-\(2\) POVMs of dimension with \(2\) inputs and \(2\) 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]]
References
- Parameters:
dim (int) – The dimensions of the measurements.
num_inputs (int) – The number of inputs for the measurement.
num_outputs (int) – The number of outputs for the measurement.
- Returns:
A set of dim-by-dim POVMs of shape (dim, dim, num_inputs, num_outputs).
- Return type:
numpy.ndarray