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

V rho conj mul self eq

V_rho_conj_mul_self_eq

Plain-language statement

V_rho^H * V_rho simplifies to sandwiching the traceRight by the inverse square root.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

V rho isometry

V_rho_isometry

Plain-language statement

V_rho is an isometry.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

W mat sq le one

W_mat_sq_le_one

Plain-language statement

Core inequality: W†W ≤ I. This is the key step, following from the isometry argument: V_rho ⊗ I_C and I_A ⊗ V_sigma are isometries, their cross product has norm ≤ 1, and the result can be related to W_mat through the MES computation (Eq. 6 in Lin-Kim-Hsieh).

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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