Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 15 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.28.0

Operator ineq SSA

operator_ineq_SSA

Plain-language statement

Operator extension of SSA (Main result of Lin-Kim-Hsieh). For positive definite ρ_AB and σ_BC: ρ_A⁻¹ ⊗ σ_BC ≤ ρ_AB⁻¹ ⊗ σ_C where ρ_A = Tr_B(ρ_AB) and σ_C = Tr_B(σ_BC), and the RHS is reindexed via the associator (dA × dB) × dC ≃ dA × (dB × dC).

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Pos Def trace Right

PosDef_traceRight

Plain-language statement

The partial trace (left) of a positive definite matrix is positive definite.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Sᵥₙ pure tripartite triangle

Sᵥₙ_pure_tripartite_triangle

Plain-language statement

Triangle inequality for pure tripartite states: S(A) ≤ S(B) + S(C).

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Sᵥₙ subadditivity

Sᵥₙ_subadditivity

Plain-language statement

"Ordinary" subadditivity of von Neumann entropy

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Sᵥₙ wm

Sᵥₙ_wm

Plain-language statement

Weak monotonicity, version with partial traces.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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