Private communication from Pauli channels with no privacy
Abstract
A channel capacity quantifies the communication capability of a noisy physical process. In contrast to communication channels in the classical world, quantum theory makes this capability contextual. We show that two Pauli two-qubit channels, each with zero private classical capacity, can be used to transmit private information when used together. One is a two-qubit Pauli channel whose environment can reconstruct the receiver output up to matrix transposition; the other is an antidegradable channel. We obtain a similar result when the second channel is the 50% qubit erasure channel. A simple binary code built from rank-three mixtures of Bell states activates private communication. The main ingredient in our construction is a transpose-antidegradable channel that is not antidegradable.
Related
- The exact strong converse exponent for private communication over quantum channels
- Private communication via zero-private-capacity quantum channels
- An exponential strong converse for private communication over degradable quantum channels
- Optimal quantum locally differentially private mechanisms in the high-privacy regime
- Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry
BibTeX
@misc{uthirakalyani2026private,
title = {{Private communication from Pauli channels with no privacy}},
author = {Uthirakalyani G and Pritam Halder and David Elkouss},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20133},
eprint = {2609.20133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20133},
}
RIS
TY - UNPB
TI - Private communication from Pauli channels with no privacy
AU - Uthirakalyani G
AU - Pritam Halder
AU - David Elkouss
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20133
UR - https://arxiv.org/abs/2609.20133
AB - A channel capacity quantifies the communication capability of a noisy physical process. In contrast to communication channels in the classical world, quantum theory makes this capability contextual. We show that two Pauli two-qubit channels, each with zero private classical capacity, can be used to transmit private information when used together. One is a two-qubit Pauli channel whose environment can reconstruct the receiver output up to matrix transposition; the other is an antidegradable channel. We obtain a similar result when the second channel is the 50% qubit erasure channel. A simple binary code built from rank-three mixtures of Bell states activates private communication. The main ingredient in our construction is a transpose-antidegradable channel that is not antidegradable.
ER -