finite.works
Results · Quantum channels and memory

Causal quantum-channel simulation: memory beyond entropy

Seth Douglas and Nidhal Mghirbi · version 1.1.2 · Zenodo, · doi:10.5281/zenodo.23070870 · PDF

In plain wordsTwo quantum channels that agree on the usual one-use measures can differ in memory: applied n times, each output released before the next input and at the same qubit exchange, one needs five memory qubits for any n, the other memory growing like a power of n.

The result

As the paper states it, in briefTwo explicit channels with the same complete Choi spectrum and the same entropies need different amounts of memory at the same optimal exchange rate.

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Novelty and credit

Novelty
Extends named prior work: its entropy bookkeeping extends the subadditivity argument of Rybár and Ziman, Kretschmann and Werner and Bisio, D’Ariano, Perinotti, Chiribella and Sedlák are credited for memory channels and minimal memory, and its purity theorem proves the converse of an implication in Bath dimension and initial entropy.

Versionsfour, each with its own DOI

Every archived version, newest first. Dates are Zenodo publication dates. All versions: 10.5281/zenodo.23027626, which always resolves to the newest.
VersionDateDOINotes
1.1.210.5281/zenodo.23070870Correction: Credit and scope: that the cost vanishes on the closure of finite tracial factorizations is credited to the closed-device preprint, and this paper proves the converse; “polynomial memory at every exchange rate” is scoped to purity limited to O(log n); Watrous is credited for a relative-interior fact. PDF hosted here.
1.1.110.5281/zenodo.23065791
1.1.010.5281/zenodo.23048998
1.0.010.5281/zenodo.23027627

Paper, code and links

PDF

papers/memory-beyond-entropy-v1.1.2.pdf, version 1.1.2, 1,248,988 bytes.

SHA-256 f94055e398a1507aaf7c2b98fe4c34db0394ad82cccfcb3ee8c7a9cc22113894

Corrections

  1. Version 1.1.2. Credit and scope: that the cost vanishes on the closure of finite tracial factorizations is credited to the closed-device preprint, and this paper proves the converse; “polynomial memory at every exchange rate” is scoped to purity limited to O(log n); Watrous is credited for a relative-interior fact.doi:10.5281/zenodo.23070870

All corrections, and what counts as one.

Cite

@misc{douglas2026memorybeyondentropy,
  author  = {Douglas, Seth and Mghirbi, Nidhal},
  title   = {Causal quantum-channel simulation: memory beyond entropy},
  year    = {2026},
  version = {1.1.2},
  doi     = {10.5281/zenodo.23070870},
  url     = {https://doi.org/10.5281/zenodo.23070870}
}

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