Change photon_number_expectation

[dorakingx]

Before submitting

Please complete the following checklist when submitting a PR:

• All new features must include a unit test.
  If you've fixed a bug or added code that should be tested, add a test to the
  tests directory!

• All new Python code must be clearly commented and documented.
  If you do make documentation changes, make sure that the docs build and
  render correctly by running make docs.

• Ensure that the test suite passes, by running make test.

• Add a new entry to the .github/CHANGELOG.md file, summarizing the
  change, and including a link back to the PR.

• The Walrus source code conforms to
  PEP8 standards.
  We check all of our code against Pylint.
  To lint modified files, simply pip install pylint, and then
  run pylint thewalrus/path/to/file.py.

When all the above are checked, delete everything above the dashed
line and fill in the pull request template.

---

Context:

Description of the Change:

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[nquesada]

Is this related to this bug: #336 ?

[dorakingx]

No, it's not. When calculating the variance of third-body correlations, I needed to compute the expected value of polynomial products such as N_1^2N_2 . However, I was only able to handle cases where all exponents were either 1 or 2. Therefore, I modified the photon_number_expectation function to allow for the calculation of expected values with a wider range of exponents.

[nquesada]

Understood. You will need to add new tests in test_quantum.py and make sure to pass pylint and black on the PR. Finally, should you be interested in the theory behind photon_number_moments, we wrote a paper explaining all sort of useful properties: https://arxiv.org/abs/2212.06067 .

[nquesada]

Hi @dorakingx: are you planning to add a unit test for your proposed changes?

[dorakingx]

Actually, since my project no longer requires calculating the expected value of polynomial products, I don't plan to add any tests.