High privacy limits quantum channels ability to keep entanglement
High quantum local differential privacy breaks entanglement
Cryptography and SecurityInformation Theory
Summary
Differential privacy is a way to protect sensitive data, and quantum entanglement is a key resource in quantum computing. The authors studied how strong privacy rules affect quantum channels, which process quantum information. They found that when local differential privacy is very strict, the quantum channel cannot keep entanglement intact—it basically breaks it. This finding means that quantum protocols requiring entanglement won't work well under very high privacy constraints.
What this means in practice
- •For quantum algorithm developers: Avoid designing quantum protocols that rely on entanglement when strong local privacy noise is involved, as entanglement will be destroyed.
- •For quantum machine learning engineers: Simulate learning algorithms with quantum memory under strong privacy noise by classical single-copy measurements, simplifying implementation.
A theory result. No direct application yet.
Authors
Sujeet Bhalerao, Theshani Nuradha, Felix Leditzky
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 $\varepsilon$-QLDP channel with a $d$-dimensional input is entanglement-breaking whenever $\varepsilon\leq\log\frac{d}{d-1}$. We also prove an approximate version for $(\varepsilon,δ)$-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.