High quantum local differential privacy breaks entanglement
Abstract
Differential privacy provides a mathematical framework for guaranteeing privacy for sensitive data. In quantum information processing, the interaction of privacy constraints with quantum resources such as entanglement remains a question of interest. Given that the utility of many protocols, and often the presence of a quantum advantage, relies on quantum resources such as entanglement, it is crucial to understand when a privacy requirement for a quantum channel is compatible with the channel's ability to preserve entanglement. We study this question for quantum local differential privacy (QLDP). Our main result shows that every ε-QLDP channel with a d-dimensional input is entanglement-breaking whenever ε≤logd/(d−1). We also prove an approximate version for (ε,δ)-QLDP, where channels in the same high-privacy regime are close in diamond norm to an entanglement-breaking channel. We further prove a composition result for a collection of private quantum channels having entangled inputs and global measurements in the high-privacy regime. Finally, we apply our results to private quantum learning theory. We prove that any learning protocol using arbitrary quantum memory on copies of the output of an entanglement-breaking channel can be simulated by a protocol that measures the corresponding unprocessed input copies one at a time while storing only classical information. Combining this result with our high-privacy entanglement-breaking theorem, we show that under sufficiently private local noise, a learning protocol with quantum memory for purity testing and bipartite product testing is subject to the sample complexity lower bounds for protocols with single-copy measurements on the noiseless tasks. We also obtain stronger sample complexity lower bounds when a single highly private channel acts on the entire multipartite input.
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BibTeX
@misc{bhalerao2026high,
title = {{High quantum local differential privacy breaks entanglement}},
author = {Sujeet Bhalerao and Theshani Nuradha and Felix Leditzky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13418},
eprint = {2609.13418},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13418},
}
RIS
TY - UNPB
TI - High quantum local differential privacy breaks entanglement
AU - Sujeet Bhalerao
AU - Theshani Nuradha
AU - Felix Leditzky
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13418
UR - https://arxiv.org/abs/2609.13418
AB - Differential privacy provides a mathematical framework for guaranteeing privacy for sensitive data. In quantum information processing, the interaction of privacy constraints with quantum resources such as entanglement remains a question of interest. Given that the utility of many protocols, and often the presence of a quantum advantage, relies on quantum resources such as entanglement, it is crucial to understand when a privacy requirement for a quantum channel is compatible with the channel's ability to preserve entanglement. We study this question for quantum local differential privacy (QLDP). Our main result shows that every ε-QLDP channel with a d-dimensional input is entanglement-breaking whenever ε≤logd/(d−1). We also prove an approximate version for (ε,δ)-QLDP, where channels in the same high-privacy regime are close in diamond norm to an entanglement-breaking channel. We further prove a composition result for a collection of private quantum channels having entangled inputs and global measurements in the high-privacy regime. Finally, we apply our results to private quantum learning theory. We prove that any learning protocol using arbitrary quantum memory on copies of the output of an entanglement-breaking channel can be simulated by a protocol that measures the corresponding unprocessed input copies one at a time while storing only classical information. Combining this result with our high-privacy entanglement-breaking theorem, we show that under sufficiently private local noise, a learning protocol with quantum memory for purity testing and bipartite product testing is subject to the sample complexity lower bounds for protocols with single-copy measurements on the noiseless tasks. We also obtain stronger sample complexity lower bounds when a single highly private channel acts on the entire multipartite input.
ER -