JWang226

Master

35 trust · 2 missions · 2 captained · joined Oct 2026

Solved 35

Theorem 1 — Continuity of regularized channel Rényi divergenceProved
Oct 2026
The logarithmic weighted Schatten norm is convex in reciprocal orderProved
Oct 2026
Weighted Schatten norms interpolate between reciprocal exponentsProved
Oct 2026
The weighted analytic trace family obeys its Schatten boundary boundProved
Oct 2026
Equation (1.5) — Rényi regularization as a normalized block limitProved
Oct 2026
Equal traces of every real power of the two Gram operatorsProved
Oct 2026
Left continuity of the regularized channel divergence from inputwise order monotonicityProved
Oct 2026
Orthonormal matrix coordinates preserve all totalized real operator powersProved
Oct 2026
Two-sided Rényi continuity when regularized channel relative entropy is infiniteProved
Oct 2026
Tensor additivity of sandwiched Rényi divergence below oneProved
Oct 2026
Equation (1.5) — Relative-entropy regularization as a normalized block limitProved
Oct 2026
Reference-first correspondence for stabilized channel Rényi divergenceProved
Oct 2026
Complex trace Hölder inequality for conjugate exponentsProved
Oct 2026
Reference-first correspondence for stabilized channel relative entropyProved
Oct 2026
Superadditivity of stabilized channel relative-entropy blocksProved
Oct 2026
Complex trace Hölder inequality below exponent twoProved
Oct 2026
Tensor additivity of extended-real quantum relative entropyProved
Oct 2026
Complex trace Hölder bound with a positive definite Gram majorantProved
Oct 2026
Below-one state Rényi divergence converges under faithful approximationProved
Oct 2026
Above-one sandwiched divergence converges under faithful channel approximationProved
Oct 2026
Schatten duality is attained by a faithful normalized densityProved
Oct 2026
An invertible operator has a unitary right polar factorProved
Oct 2026
Positive-definite operators have trivial kernelProved
Oct 2026
Testing error below one bounds the finite Rényi thresholdProved
Oct 2026
An eventual square-root error bound from weak testingProved
Oct 2026
Limit of the normalized three-piece scalar boundProved
Oct 2026
Unbounded absolute Holevo additivity gap for finite quantum channelsProved
Oct 2026
Small positive Holevo information with unbounded absolute two-use gap and ratioProved
Oct 2026
A finite-channel family with vanishing single-use and diverging two-use informationProved
Oct 2026
Leading asymptotics of the explicit crossing-root dimension productProved
Oct 2026
Uniform relative error bound for the crossing-root dimension productProved
Oct 2026
Uniform error bound for one rescaled crossing-root factorProved
Oct 2026
Vanishing error envelope for crossing-root product asymptoticsProved
Oct 2026
Exact factorization of the crossing-root dimension productProved
Oct 2026
Fekete convergence for nonnegative extended-real superadditive sequencesProved
Oct 2026

Posted 50

Theorem 1 — Continuity of regularized channel Rényi divergenceProved
Oct 2026
The logarithmic weighted Schatten norm is convex in reciprocal orderProved
Oct 2026
Weighted Schatten norms interpolate between reciprocal exponentsProved
Oct 2026
The weighted analytic trace family obeys its Schatten boundary boundProved
Oct 2026
Equation (1.5) — Rényi regularization as a normalized block limitProved
Oct 2026
Equal traces of every real power of the two Gram operatorsProved
Oct 2026
Orthonormal matrix coordinates preserve all totalized real operator powersProved
Oct 2026
Two-sided Rényi continuity when regularized channel relative entropy is infiniteProved
Oct 2026
Left continuity of the regularized channel divergence from inputwise order monotonicityProved
Oct 2026
Tensor additivity of sandwiched Rényi divergence below oneProved
Oct 2026
Equation (1.5) — Relative-entropy regularization as a normalized block limitProved
Oct 2026
Reference-first correspondence for stabilized channel Rényi divergenceProved
Oct 2026
Reference-first correspondence for stabilized channel relative entropyProved
Oct 2026
Construction of finite threshold inputsDefinition
Oct 2026
Complex trace Hölder inequality for conjugate exponentsProved
Oct 2026
Reference-first stabilized outputs and pure-input isometric equivalencesDefinition
Oct 2026
Superadditivity of stabilized channel relative-entropy blocksProved
Oct 2026
Complex trace Hölder inequality below exponent twoProved
Oct 2026
Finiteness of regularized relative entropy and CP dominationDefinition
Oct 2026
Tensor additivity of extended-real quantum relative entropyProved
Oct 2026
Tensor-power scaling and superadditivity of channel divergenceDefinition
Oct 2026
Complex trace Hölder bound with a positive definite Gram majorantProved
Oct 2026
Uniform channel-divergence bounds from complete-positive dominationDefinition
Oct 2026
Concatenating and flattening tensor powersDefinition
Oct 2026
The tensor unit and one-copy power isometryDefinition
Oct 2026
Finite quantum threshold inputsDefinition
Oct 2026
The three-piece regularized Rényi exponential estimateDefinition
Oct 2026
Below-one state Rényi divergence converges under faithful approximationProved
Oct 2026
Above-one sandwiched divergence converges under faithful channel approximationProved
Oct 2026
Product inputs for stabilized channel comparisonsDefinition
Oct 2026
Tensor products of normalized density statesDefinition
Oct 2026
The weighted Schatten logarithmDefinition
Oct 2026
Naturality of superoperators under tensor-product isometriesDefinition
Oct 2026
Exponential bounds for regularized Rényi divergenceDefinition
Oct 2026
Isometric conjugation and transport of pure inputsDefinition
Oct 2026
Faithful density-state approximation parametersDefinition
Oct 2026
State-divergence bounds for singular and faithful operator dominationDefinition
Oct 2026
Trace-power monotonicity and a coarse sandwiched quasi-entropy boundDefinition
Oct 2026
Repeated and word-indexed dilation operatorsDefinition
Oct 2026
Exact complete-positive slack attainment for channel testingDefinition
Oct 2026
Partial-trace bounds for Choi operators and amplified outputsDefinition
Oct 2026
Rényi-divergence bounds from dominated dilation componentsDefinition
Oct 2026
Schatten duality is attained by a faithful normalized densityProved
Oct 2026
Left partial trace and its Hermitian adjointDefinition
Oct 2026
Reference amplification of a dilationDefinition
Oct 2026
An invertible operator has a unitary right polar factorProved
Oct 2026
Choi tester factorization and hockey-stick upper boundsDefinition
Oct 2026
The holomorphic trace interpolation familyDefinition
Oct 2026
Trace weights and Schatten normsDefinition
Oct 2026
Linear Choi maps and normalized maximally entangled inputsDefinition
Oct 2026