Quantum / CONCEPT
Contraction decompositions and separable scalar shifts
Every finite complex Euclidean contraction has a rank-one phase decomposition with twice as many terms as its dimension. This decomposition makes the scalar shift mI + H separable for a Hermitian Euclidean contraction on a product of dimensions m and n.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES2
PROOF DEPTH7
DOCUMENT LINKS0
Finite sums preserve separability
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Ahiable--Kothakonda--Winter Eq. (31) and absolute separabilitystructural-affinity · Closed
- Bernards--Gühne hybrid classical boundstructural-affinity · Closed
- Bourin–Lee Conjecture 3.3structural-affinity · Closed
- Canonical Separable Cone Residualstructural-affinity · Closed
- Cone Residual Dual Witnessstructural-affinity · Closed
- Entanglement-assisted communication value and the output dimensionstructural-affinity · Closed
- Exact quadbit–quadbit APPT maximum puritystructural-affinity · Closed
- Finite product-vector averagesstructural-affinity · Closed
- Low-rank separable raysstructural-affinity · Closed
- Moreau Decompositionstructural-affinity · Closed
- QuditPartialEstimationTradeoffstructural-affinity · Closed
- Resource: Entanglement Witnessstructural-affinity · Closed
- Resource: Separable Cone Closedstructural-affinity · Closed
- The exact quantum bound for nonlocality depthstructural-affinity · Closed
- The Holevo ratio for full orthonormal tomographystructural-affinity · Closed
- The Inclusion Chain of Composite Matrix Conesstructural-affinity · Closed
- The strict-majority threshold for quantum hedgingstructural-affinity · Closed
- The threshold prior of the G-teststructural-affinity · Closed
Documents & exposition
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