Feature: Pretty Good Measurement

[vprusso]

Given a collection of vectors or matrices representing quantum states, compute the corresponding "pretty good measurement".

A formal definition of the "pretty good measurement" can be found in Section 3.1 (page 137; "The pretty good measurement") of John Watrous's textbook.

In order to define the pretty good measurement, one must first construct the "average state" (simply sum up the density operators in your collection) as specified in Equation 3.49. Then, compute the pretty good measurement by way of either Equation 3.50 (if the average state is positive definite) or by way of Equation 3.52 (if the average state is not positive definite).

Note that computing negative fractional powers of matrices will benefit from the scipy.linalg.fractional_matrix_power function (documentation here)

The functionality for this should be created in measurements/pretty_good_measurement.py with corresponding unit tests found in tests/test_measurements/test_pretty_good_measurement.py. Be sure to also update the docs in /docs/measurements.rst under "Measurements" with toqito.measurements.pretty_good_measurement.py.