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

1 topic

8 results

Clear filters
Project-declaredLean 4.28.0

Dual choi matrix

MatrixMap.dual_choi_matrix

Plain-language statement

The Choi matrix of the dual map is the transpose of the reindexed Choi matrix of the original map.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

View proof record
Project-declaredLean 4.28.0

Dual kron

MatrixMap.dual_kron

Plain-language statement

The dual of a Kronecker product of maps is the Kronecker product of their duals.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

View proof record
Project-declaredLean 4.28.0

Dual unique

MatrixMap.dual_unique

Plain-language statement

If two matrix maps satisfy the trace duality property, they are equal.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

View proof record
Project-declaredLean 4.28.0

Dual Unital

MatrixMap.dual_Unital

Plain-language statement

The dual of TracePreserving map is not trace-preserving, it's unital, that is, M*(I) = I.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

View proof record
Project-declaredLean 4.28.0

Is Positive dual

MatrixMap.IsPositive.dual

Plain-language statement

The dual of a IsPositive map also IsPositive.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

View proof record