Quantum Local Differential Privacy and Quantum Statistical Query Model
- URL: http://arxiv.org/abs/2203.03591v2
- Date: Mon, 21 Aug 2023 22:25:13 GMT
- Title: Quantum Local Differential Privacy and Quantum Statistical Query Model
- Authors: Armando Angrisani and Elham Kashefi
- Abstract summary: Quantum statistical queries provide a theoretical framework for investigating the computational power of a learner with limited quantum resources.
In this work, we establish an equivalence between quantum statistical queries and quantum differential privacy in the local model.
We consider the task of quantum multi-party computation under local differential privacy.
- Score: 0.7673339435080445
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum statistical queries provide a theoretical framework for investigating
the computational power of a learner with limited quantum resources. This model
is particularly relevant in the current context, where available quantum
devices are subject to severe noise and have limited quantum memory. On the
other hand, the framework of quantum differential privacy demonstrates that
noise can, in some cases, benefit the computation, enhancing robustness and
statistical security. In this work, we establish an equivalence between quantum
statistical queries and quantum differential privacy in the local model,
extending a celebrated classical result to the quantum setting. Furthermore, we
derive strong data processing inequalities for the quantum relative entropy
under local differential privacy and apply this result to the task of
asymmetric hypothesis testing with restricted measurements. Finally, we
consider the task of quantum multi-party computation under local differential
privacy. As a proof of principle, we demonstrate that the parity function is
efficiently learnable in this model, whereas the corresponding classical task
requires exponentially many samples.
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