The memory and purity cost of immediate delivery
In plain wordsReleasing each output before the next input arrives has a price: a device applying a particular quantum channel n times needs purity proportional to n, against almost none for batch release, while many channels that finite, maximally mixed memories implement or approximate need memory well below n.
The result
As the paper states it, in briefHow many qubits a device must keep, exchange and be given pure to apply one channel times when each output must leave before the next input arrives.
Questionson the index
- Answered Which unital channels are repeatable by one device with a finite memory and no resets? posed by others
How this was checked
- Machine checks
- Scripts that check the listed statements; they do not replace the proofs.
- Lean
- None.
- Peer review
- Not yet.
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Novelty and credit
- Novelty
- Extends named prior work: its model extends the no-reset setting of Rybár and Ziman, and with the catalytic dilation of Lie, Son, Boes, Ng and Wilming it answers their question on repeatable unital channels; Haagerup and Musat’s results are credited where used.
Versionsone, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| 1.0.0 | 10.5281/zenodo.23198907 | PDF hosted here. |
Paper, code and links
papers/immediate-delivery-v1.0.0.pdf, version 1.0.0, 1,678,356 bytes.SHA-256 95ffecb7eeadf382ca80faba667a4ab8448f2a4aecfa73110bfb19899d7ab051
Corrections
None so far.
All corrections, and what counts as one.
Cite
@misc{douglas2026immediatedelivery,
author = {Douglas, Seth and Mghirbi, Nidhal},
title = {The memory and purity cost of immediate delivery},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.23198907},
url = {https://doi.org/10.5281/zenodo.23198907}
}