States, expectation, and uncertainty relations

[TomOleDiem]

Adds states and the uncertainty relations built on the existing Jordan/Lie observable API.

• OperatorAlgebra.Measurement.State: the expectation functional ω⟨a⟩, centering, covariance, and variance.
• OperatorAlgebra.Measurement.Uncertainty: the GNS Cauchy–Schwarz inequality for states, and the Robertson–Schrödinger and Robertson uncertainty relations.

[github-actions]

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[jstoobysmith]

Maybe in this we can also subsume the definitions and lemmas within ./Operators/StateObservables/ where possible?
I.e. remove the overlap

[jstoobysmith]

Putting on

awaiting-author

for the comment above

[TomOleDiem]

Maybe in this we can also subsume the definitions and lemmas within ./Operators/StateObservables/ where possible? I.e. remove the overlap

I dont think it is time for that.
There is no notion of an unbounded operator yet.
Average position can not be defined by this PR.
Only finite systems and maybe some infinite lattice models with bounded gap can be handled as of right now.

[TomOleDiem]

-awaiting-author

[jstoobysmith]

One quick comment from me here.

[jstoobysmith]

Should "State" really be under "Measurement"?

[malmortieus537]

I see what you mean. I’m using the Heisenberg view, where states act on observables by assigning expectation values, so grouping them with measurement seemed natural.

[jstoobysmith]

Ok, can we put a comment to this effect in the doc-string?

[jstoobysmith]

awaiting-author

[malmortieus537]

-awaiting-author

[jstoobysmith]

awaiting-author

For the comment above.

[jstoobysmith]

@TomOleDiem Just a ping about the comment above

[TomOleDiem]

Superseded by #1590, which isolates the reviewed primitive API split.