feat(PhyslibAlpha): Robertson–Schrödinger for density states and ofDensity_rankOne

[naype888-cloud]

Following the discussion on #1587: the algebraic robertson_schrodinger already covers mixed states, since ofDensity is a state on H →L[ℂ] H. This PR makes that explicit, writing the uncertainty quantities of a density state as traces against ρ, and connects it to the vector-state file from #1660 by showing that vector states are the rank-one density states. Everything goes through the existing CStarAlgebra.Uncertainty API; no new definitions.

Reviewer map, in file order (PhyslibAlpha/AlgebraicFramework/HilbertSpace/State/DensityUncertainty.lean, new):

• A. expectation_ofDensity, covariance_ofDensity, variance_ofDensity: ⟨a⟩ = Re Tr(a ρ) and Cov/Var = Re Tr(δa δb ρ) with δa = centered a.
• B. robertson_schrodinger_ofDensity: robertson_schrodinger for ofDensity, stated entirely in traces.
• C. trace_rankOne_self, ofDensity_rankOne (finite-dimensional H): Tr |ψ⟩⟨ψ| = 1 for a unit vector, and ofDensity of |ψ⟩⟨ψ| equals ofVec.
• PhyslibAlpha.lean: registers the new module. No declarations removed.

AI assistance: developed with Claude (Anthropic). I have reviewed every statement and certify it.

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[naype888-cloud]

hy guys i finish timeroot and joseph observation inside this one new PR, let this one describes the robertson-schroedinguer clasical inequality, mixed states with "p" density.
plus prooves the pure states are a particular case rank one, so this conect with #1660.

this isn'a new poove, acctualy rehuse the Robertson-Schroedinguer canonical, becouse any "p" possitive with trace one all ready it's an state (ofDensity)

[jstoobysmith]

This looks good to me. I've approved. Many thanks.