Optimal quantum locally differentially private mechanisms in the high-privacy regime
Abstract
We optimize the trade-off between privacy and utility in the high-privacy regime. We adopt local differential privacy (LDP) and its quantum extension, quantum local differential privacy (QLDP), for privacy protection, and investigate utility functions including the Holevo information (which reduces to the mutual information in the classical case) and the error exponents in symmetric and asymmetric hypothesis testing. Under the LDP and QLDP constraints, these utility functions have classical and quantum optimal values, which we denote simply by C and Q, respectively, in this abstract. In this paper, we provide optimal LDP and QLDP mechanisms achieving the classical and quantum optimal values in the high-privacy regime, and prove that the asymptotic ratio Q/C in this regime takes the same value regardless of the utility function. Our results reveal quantum advantages (specifically, Q/C≥3/2) for the above utility functions when the private data take at least three possible values. In addition, conditional on a mathematical conjecture concerning equi-isoclinic tight fusion frames (EITFFs), our QLDP mechanisms also exhibit quantum advantages in a moderate-privacy regime.
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BibTeX
@misc{yoshida2026optimal,
title = {{Optimal quantum locally differentially private mechanisms in the high-privacy regime}},
author = {Yuuya Yoshida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.27278},
eprint = {2605.27278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.27278},
}
RIS
TY - UNPB
TI - Optimal quantum locally differentially private mechanisms in the high-privacy regime
AU - Yuuya Yoshida
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2605.27278
UR - https://arxiv.org/abs/2605.27278
AB - We optimize the trade-off between privacy and utility in the high-privacy regime. We adopt local differential privacy (LDP) and its quantum extension, quantum local differential privacy (QLDP), for privacy protection, and investigate utility functions including the Holevo information (which reduces to the mutual information in the classical case) and the error exponents in symmetric and asymmetric hypothesis testing. Under the LDP and QLDP constraints, these utility functions have classical and quantum optimal values, which we denote simply by C and Q, respectively, in this abstract. In this paper, we provide optimal LDP and QLDP mechanisms achieving the classical and quantum optimal values in the high-privacy regime, and prove that the asymptotic ratio Q/C in this regime takes the same value regardless of the utility function. Our results reveal quantum advantages (specifically, Q/C≥3/2) for the above utility functions when the private data take at least three possible values. In addition, conditional on a mathematical conjecture concerning equi-isoclinic tight fusion frames (EITFFs), our QLDP mechanisms also exhibit quantum advantages in a moderate-privacy regime.
ER -