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 9 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.28.0

Purify spec

MState.purify_spec

Plain-language statement

The defining property of purification, that tracing out the purifying system gives the original mixed state.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Spectrum prod

MState.spectrum_prod

Plain-language statement

Spectrum of direct product. There is a permutation σ so that the spectrum of the direct product of ρ₁ and ρ₂, as permuted under σ, is the pairwise products of the spectra of ρ₁ and ρ₂.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Spectrum pure eq constant

MState.spectrum_pure_eq_constant

Plain-language statement

The specturm of a pure state is (1,0,0,...), i.e. a constant distribution.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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