Non-Multiplicativity of the Holevo Barycenter of Quantum Channels

Abstract

The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, the multiplicativity problem asks whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although a construction is known that demonstrates the existence of channels with non-additive Holevo capacity, their corresponding Holevo barycenters still tensorize, leaving open whether multiplicativity might ultimately hold universally. Here, we answer this question in the negative by exhibiting channels for which the Holevo barycenter is not multiplicative under the tensor product of the channel with itself. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor product.

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BibTeX RIS

BibTeX

@misc{chakraborty2026nonmultiplicativity,
  title = {{Non-Multiplicativity of the Holevo Barycenter of Quantum Channels}},
  author = {Sayantan Chakraborty and Stefano Mancini and Leonardo Rossetti and Andreas Winter},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09373},
  eprint = {2609.09373},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09373},
}

RIS

TY  - UNPB
TI  - Non-Multiplicativity of the Holevo Barycenter of Quantum Channels
AU  - Sayantan Chakraborty
AU  - Stefano Mancini
AU  - Leonardo Rossetti
AU  - Andreas Winter
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09373
UR  - https://arxiv.org/abs/2609.09373
AB  - The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, the multiplicativity problem asks whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although a construction is known that demonstrates the existence of channels with non-additive Holevo capacity, their corresponding Holevo barycenters still tensorize, leaving open whether multiplicativity might ultimately hold universally. Here, we answer this question in the negative by exhibiting channels for which the Holevo barycenter is not multiplicative under the tensor product of the channel with itself. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor product.
ER  -

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