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PreprintCC BY 4.0arXiv

Fully quantum fidelity-based entropic continuity bounds

  • Matthew Simon Tan
  • Ernest Y. -Z. Tan
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Abstract

We present a continuity bound for quantum conditional entropies in terms of fidelity, with no dependence on the dimension of the conditioning system. Our results encompass both the von Neumann entropy and one version of sandwiched Rényi entropy, which is particularly relevant for applications in quantum key distribution (QKD). In such applications, this bound should provide improved results as compared to previous continuity bounds based on trace distance. We also show that the bounds can be sharpened as expected for classical-quantum states, and verify that they hold when the conditioning system has countably infinite dimension. Finally, we present several variants tailored for exponential functions of the Rényi entropies instead, which should be relevant for QKD applications.

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Cite

BibTeXRIS
BibTeX
@misc{tan2026fully,
  title = {{Fully quantum fidelity-based entropic continuity bounds}},
  author = {Matthew Simon Tan and Ernest Y. -Z. Tan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25299},
  eprint = {2610.25299},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25299},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fully quantum fidelity-based entropic continuity bounds
AU  - Matthew Simon Tan
AU  - Ernest Y. -Z. Tan
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25299
UR  - https://arxiv.org/abs/2610.25299
AB  - We present a continuity bound for quantum conditional entropies in terms of fidelity, with no dependence on the dimension of the conditioning system. Our results encompass both the von Neumann entropy and one version of sandwiched Rényi entropy, which is particularly relevant for applications in quantum key distribution (QKD). In such applications, this bound should provide improved results as compared to previous continuity bounds based on trace distance. We also show that the bounds can be sharpened as expected for classical-quantum states, and verify that they hold when the conditioning system has countably infinite dimension. Finally, we present several variants tailored for exponential functions of the Rényi entropies instead, which should be relevant for QKD applications.
ER  -