Internal modes update

[rachelchadwick]

We make changes to the internal_modes branch to:

• Make density_matrix_single_mode not include the cutoff - n=[0,cutoff) rather than n=[0,cutoff];
• Make density_matrix_single_mode return the expected dimensions even if an even cutoff is provided meaning an odd cutoff is used;
• Condense repeated functions f and f_all_charpoly into one function f_from_matrix which now calls f_from_powertrace instead of repeating this code;
• Remove distinguishable_pnr_prob.py as this function doesn't add anything that can't be done in pnr_prob and is less accurate;
• Condense three tests into one (test_distinguishable_probs, test_distinguishable_vacuum_probs, test_distinguishable_probs_collision) as they are the same with different variables;
• Order the modes in prepare_cov as we expect when the squeezing is equal (it currently reverses them).

[codecov[bot]]

Codecov Report

Merging #355 (19b0d2b) into internal_modes (adfc7ab) will increase coverage by 4.47%. The diff coverage is 30.00%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## internal_modes #355 +/- ## ================================================== + Coverage 90.69% 95.17% +4.47% ================================================== Files 32 31 -1 Lines 2386 2238 -148 ================================================== - Hits 2164 2130 -34 + Misses 222 108 -114 ``` | [Impacted Files](https://codecov.io/gh/XanaduAI/thewalrus/pull/355?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI) | Coverage Δ | | |---|---|---| | [thewalrus/\_hafnian.py](https://codecov.io/gh/XanaduAI/thewalrus/pull/355/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-dGhld2FscnVzL19oYWZuaWFuLnB5) | `94.67% <0.00%> (ø)` | | | [thewalrus/internal\_modes/\_\_init\_\_.py](https://codecov.io/gh/XanaduAI/thewalrus/pull/355/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-dGhld2FscnVzL2ludGVybmFsX21vZGVzL19faW5pdF9fLnB5) | `100.00% <ø> (ø)` | | | [thewalrus/internal\_modes/pnr\_statistics.py](https://codecov.io/gh/XanaduAI/thewalrus/pull/355/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-dGhld2FscnVzL2ludGVybmFsX21vZGVzL3Bucl9zdGF0aXN0aWNzLnB5) | `50.84% <0.00%> (ø)` | | | [thewalrus/internal\_modes/utils.py](https://codecov.io/gh/XanaduAI/thewalrus/pull/355/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-dGhld2FscnVzL2ludGVybmFsX21vZGVzL3V0aWxzLnB5) | `63.15% <ø> (+23.15%)` | :arrow_up: | | [thewalrus/internal\_modes/fock\_density\_matrices.py](https://codecov.io/gh/XanaduAI/thewalrus/pull/355/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-dGhld2FscnVzL2ludGVybmFsX21vZGVzL2ZvY2tfZGVuc2l0eV9tYXRyaWNlcy5weQ==) | `29.76% <16.66%> (+0.35%)` | :arrow_up: | | [thewalrus/internal\_modes/prepare\_cov.py](https://codecov.io/gh/XanaduAI/thewalrus/pull/355/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-dGhld2FscnVzL2ludGVybmFsX21vZGVzL3ByZXBhcmVfY292LnB5) | `100.00% <100.00%> (ø)` | | ------ [Continue to review full report at Codecov](https://codecov.io/gh/XanaduAI/thewalrus/pull/355?src=pr&el=continue&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI). > **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI) > `Δ = absolute (impact)`, `ø = not affected`, `? = missing data` > Powered by [Codecov](https://codecov.io/gh/XanaduAI/thewalrus/pull/355?src=pr&el=footer&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI). Last update [adfc7ab...19b0d2b](https://codecov.io/gh/XanaduAI/thewalrus/pull/355?src=pr&el=lastupdated&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI).

[nquesada]

Some comment on what this PR does would be helpful for the reviewer @rachelchadwick