Quantum / CONCEPT
The trace norm and its two-dimensional formula
The trace norm supplies a unitarily invariant norm in every finite complex dimension, with an exact determinant formula in dimension two.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES6
PROOF DEPTH3
DOCUMENT LINKS0
The determinant of the positive absolute value
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A counterexample to mixed-power norm monotonicitytruth-dependency · Closed
- Biased post-processed improvements are not faithfultruth-dependency · Closed
- Strict separation of measured and Uhlmann average fidelitiestruth-dependency · Closed
- The three-state root-fidelity Holevo boundtruth-dependency · Closed
- The two-qubit SVD entanglement entropy lower boundtruth-dependency · Closed
- Two unbounded entanglement gaps with one qubittruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A counterexample to mixed-power norm monotonicitystructural-affinity · Closed
- A repeated five-site potential refutes odd-period regularitystructural-affinity · Closed
- Balanced Unitary Sumstructural-affinity · Closed
- Biased post-processed improvements are not faithfulstructural-affinity · Closed
- Continuity and balanced scalar optimizationstructural-affinity · Closed
- Crossing-Matrix Determinant Obstructionstructural-affinity · Closed
- MajorizationTransferstructural-affinity · Closed
- Power Traces from Trace and Determinant in Size Twostructural-affinity · Closed
- Rank-one Hadamard products and nonnegative diagonal weightsstructural-affinity · Closed
- Reciprocal Tails of Generalized Fibonacci Numbersstructural-affinity · Closed
- Strict separation of measured and Uhlmann average fidelitiesstructural-affinity · Closed
- The three-state root-fidelity Holevo boundstructural-affinity · Closed
- The two-qubit SVD entanglement entropy lower boundstructural-affinity · Closed
- Two unbounded entanglement gaps with one qubitstructural-affinity · Closed
- Unitarily invariant norms and symmetric diagonal gaugesstructural-affinity · Closed
- Weil: Pos Indexstructural-affinity · Closed
- Zero Norm Propagation for Matrix Statesstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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