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The fixed-particle admissible Hermitian density domain
Definition
For and , let and be as in Rank-r orthogonal projector domain. The admissible fixed-particle density domain is where means for every , and means . A member of need not be idempotent. The matrix norm and metric used below are the Frobenius norm and its induced metric. Every rank- orthogonal projector is in by Every rank-r orthogonal projector is an admissible density ↗.
Depends on
- Rank-r orthogonal projector domain
- Self-adjoint and normal endomorphisms of a finite-dimensional real or complex inner product space
- Rectangular matrix multiplication and the identity matrix $I_n$, including zero-sized shapes
- The trace $\operatorname{tr}(A)$ as the sum of the diagonal entries
- The Frobenius norm $\lVert A\rVert_F=(\sum_{i,j}|a_{ij}|^2)^{1/2}$ on real or complex matrices
Used by
- Finite-budget relaxed density-matrix mixing Algorithm
- A convex density mixture can be admissible without being a projector Example
- Density mixing preserves admissibility but need not preserve idempotence Lemma
- Every rank-r orthogonal projector is an admissible density Lemma
- The admissible Hermitian density domain is closed, convex, and complete Lemma
- A uniform derivative bound certifies contraction of relaxed density mixing Theorem
Dependency tree · two levels
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