TY - JOUR

T1 - Quantum Differential Privacy

T2 - An Information Theory Perspective

AU - Hirche, Christoph

AU - Rouze, Cambyse

AU - Franca, Daniel Stilck

N1 - Funding Information: This work was supported by the European Union's Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie under Grant H2020-MSCA-IF-2020-101025848. The work of Cambyse Rouzé was supported in part by the Junior Researcher START Fellowship from the Munich Center for Quantum Science and Technology; and in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy under Grant EXC-2111 390814868. The work of Daniel Stilck Franca was supported in part by the VILLUM FONDEN via the QMATH Centre of Excellence under Grant 10059 and in part by the QuantERA ERA-NET Cofund in Quantum Technologies implemented within the European Union's Horizon 2020 Program (QuantAlgo Project) via the Innovation Fund Denmark and from the European Research Council under Grant 81876.

PY - 2023/9/1

Y1 - 2023/9/1

N2 - Differential privacy has been an exceptionally successful concept when it comes to providing provable security guarantees for classical computations. More recently, the concept was generalized to quantum computations. While classical computations are essentially noiseless and differential privacy is often achieved by artificially adding noise, near-term quantum computers are inherently noisy and it was observed that this leads to natural differential privacy as a feature. In this work we discuss quantum differential privacy in an information theoretic framework by casting it as a quantum divergence. A main advantage of this approach is that differential privacy becomes a property solely based on the output states of the computation, without the need to check it for every measurement. This leads to simpler proofs and generalized statements of its properties as well as several new bounds for both, general and specific, noise models. In particular, these include common representations of quantum circuits and quantum machine learning concepts. Here, we focus on the difference in the amount of noise required to achieve certain levels of differential privacy versus the amount that would make any computation useless. Finally, we also generalize the classical concepts of local differential privacy, Rényi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.

AB - Differential privacy has been an exceptionally successful concept when it comes to providing provable security guarantees for classical computations. More recently, the concept was generalized to quantum computations. While classical computations are essentially noiseless and differential privacy is often achieved by artificially adding noise, near-term quantum computers are inherently noisy and it was observed that this leads to natural differential privacy as a feature. In this work we discuss quantum differential privacy in an information theoretic framework by casting it as a quantum divergence. A main advantage of this approach is that differential privacy becomes a property solely based on the output states of the computation, without the need to check it for every measurement. This leads to simpler proofs and generalized statements of its properties as well as several new bounds for both, general and specific, noise models. In particular, these include common representations of quantum circuits and quantum machine learning concepts. Here, we focus on the difference in the amount of noise required to achieve certain levels of differential privacy versus the amount that would make any computation useless. Finally, we also generalize the classical concepts of local differential privacy, Rényi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.

KW - data privacy

KW - differential privacy

KW - Quantum computing

KW - quantum information science

UR - http://www.scopus.com/inward/record.url?scp=85159801876&partnerID=8YFLogxK

U2 - 10.1109/TIT.2023.3272904

DO - 10.1109/TIT.2023.3272904

M3 - Article

AN - SCOPUS:85159801876

VL - 69

SP - 5771

EP - 5787

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 9

ER -