finite.works
Results · Quantum channels and memory

Bath dimension and initial entropy for closed repeated use of a quantum channel

Seth Douglas · version 1.1.0 · Zenodo, · arXiv:2609.18267 · doi:10.5281/zenodo.22788806 · PDF

In plain wordsA sealed device that serves repeated uses of a quantum channel, with no resets, discards or fresh supplies, pays in two resources, memory size and starting randomness; per use, two entropy quantities fix the exact trade-off, and randomness can shrink the memory only to a definite floor.

The result

As the paper states it, in briefThe bath dimension and initial entropy that closed, repeated use of a quantum channel requires.

How this was checked

Blind audits
Version 1.1.0 applied the repairs of three blind reviews, which found no theorem-level defect.
Lean
A closing identity and six accounting lemmas; the rate-region theorem, entropy bounds, Gram repair, concentration and compiler are not formalized.
Peer review
Not yet.

Every check here is internal. How we check results.

Novelty and credit

Novelty
New, with named precedent: Rybár and Ziman’s repeatable quantum memory channels are a close comparison; the known functional is the quantum privacy funnel of Datta, Hirche and Winter, and the Slepian–Wolf split is credited.

Versionstwo, each with its own DOI

Every archived version, newest first. Dates are Zenodo publication dates. All versions: 10.5281/zenodo.22779672, which always resolves to the newest.
VersionDateDOINotes
1.1.010.5281/zenodo.22788806Correction: A displayed lower bound, 0.045566, had been rounded up from 0.0455659970, and a growth remark failed at r = 0. Version 1.1.0 uses a stronger exact witness and restates the remark. PDF hosted here.
1.0.010.5281/zenodo.22779673

Paper, code and links

PDF

papers/closed-memory-v1.1.0.pdf, version 1.1.0, 547,696 bytes.

SHA-256 a6db5c4811f6a1b747fb40e5590d58970954d92e9b98be0f27632cc8b1c2879f

Corrections

  1. Version 1.1.0. A displayed lower bound, 0.045566, had been rounded up from 0.0455659970, and a growth remark failed at r = 0. Version 1.1.0 uses a stronger exact witness and restates the remark.doi:10.5281/zenodo.22788806

All corrections, and what counts as one.

Cite

@misc{douglas2026closedmemory,
  author        = {Douglas, Seth},
  title         = {Bath dimension and initial entropy for closed repeated use of a quantum channel},
  year          = {2026},
  version       = {1.1.0},
  doi           = {10.5281/zenodo.22788806},
  url           = {https://doi.org/10.5281/zenodo.22788806},
  eprint        = {2609.18267},
  archiveprefix = {arXiv}
}

closed-memory.bibAll papers as BibTeX