bibkey: braunsteinpati2007nohiding authors: Samuel L. Braunstein and Arun K. Pati year: 2007 title: “Quantum Information Cannot Be Completely Hidden in Correlations: Implications for the Black-Hole Information Paradox” doi: 10.1103/PhysRevLett.98.080502 claim: Exact input-independent quantum output requires the purifying subsystem to retain the input information; orthonormal purification vectors give the finite-dimensional replacement capacity bound. strata_touched:

• D5/S3/Quantum/Entanglement/UniversalReplacementCapacityGrowth license: citation-only triage: anchor

No-Hiding and Universal Replacement

Braunstein and Pati’s no-hiding theorem is the literature source for the input-independent output condition and its purification-space consequence. The repository represents the exact finite-dimensional condition as UniversalReplacement and derives the orthonormal contraction family and dim B_next >= dim B_prev * rank tau in universal_replacement_capacity_growth.

The formal proof uses the repository’s finite DensityState and partialTraceFirst, then binds pinned Mathlib complex polarization, spectral decomposition, and the dimension bound for linearly independent vectors. It does not claim novelty, an approximate no-hiding result, a theorem about small corrections, or a resolution of the black-hole information paradox.

Search Log

• 2026-09-06: Crossref and the arXiv title query verified the authors, title, publication year, DOI, and gr-qc/0603046 identifier.
• 2026-09-06: Read the arXiv PDF, section “Perfect hiding processes”: equation (2) gives the spectral purification, equation (3) uses arbitrary complex superposition coefficients to annihilate cross terms, and the following paragraph constructs an orthonormal set spanning a Kd-dimensional ancilla subspace. These are the specific literature claims represented here.
• 2026-09-06: The initial guessed quant-ph/0603046 identifier resolved to an unrelated paper and was discarded; it is not a source for this note.
• 2026-09-06: No complete replacement capacity theorem was found in current D5 or pinned Mathlib. The GitHub Lean search hit physlib channel APIs, but physlib is not an admitted dependency. The local proof follows rule 11(4) without changing the dependency pins.

Verified locator

• https://doi.org/10.1103/PhysRevLett.98.080502
• https://arxiv.org/abs/gr-qc/0603046