The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
Quantum Differential Privacy: An Information Theory Perspective
5 Pith papers cite this work, alongside 3 external citations. Polarity classification is still indexing.
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abstract
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, Renyi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.
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Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
Robust protocols are identified for three quantum Shannon tasks under three notions of almost i.i.d. structure that preserve i.i.d. rates, along with new concepts of almost i.i.d. process and club distance.
The report assembles abstracts of invited talks, presentations, and posters from the FFCS conference on foundational limits and emerging paradigms in communication.
citing papers explorer
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Integral representations of $f$-divergences for general von Neumann algebras
The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
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Sufficiency and Petz recovery for positive maps
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
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Quantum Shannon theory made robust: a tale of three protocols for almost i.i.d. sources
Robust protocols are identified for three quantum Shannon tasks under three notions of almost i.i.d. structure that preserve i.i.d. rates, along with new concepts of almost i.i.d. process and club distance.
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Foundations of Future Communication Systems: Innovations in Communication - A Report
The report assembles abstracts of invited talks, presentations, and posters from the FFCS conference on foundational limits and emerging paradigms in communication.
- New approaches to almost i.i.d. information theory