Limiting one-way distillable secret key via privacy testing of extendible states

2025-11-06

AI Summary

This work investigates the fundamental security limits of quantum key extraction, focusing on the maximum success probability of privacy tests applied to arbitrary $k$-extendible states. We establish that this probability equals—exactly and without gap—the maximum fidelity between the given state and the standard maximally entangled state, thereby forging the first tight connection between privacy testing and $k$-extendibility. Leveraging this equivalence, we derive single-letter, efficiently computable upper bounds on the one-shot and asymptotic extractable key rates, which are strictly tighter than all previously known bounds. Furthermore, we unify the bounds for forward-assisted private capacity of quantum channels and for extractable key from bipartite states, and demonstrate their significant advantage over existing bounds for prototypical channels—including depolarizing and erasure channels. The core innovation lies in the synergistic integration of $k$-extendibility theory, privacy testing, and fidelity-based analysis, achieving simultaneous advances in theoretical rigor and computational tractability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Philosophy and Ethics of AI: Privacy & Security

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data

Abstract

The notions of privacy tests and $k$-extendible states have both been instrumental in quantum information theory, particularly in understanding the limits of secure communication. In this paper, we determine the maximum probability with which an arbitrary $k$-extendible state can pass a privacy test, and we prove that it is equal to the maximum fidelity between an arbitrary $k$-extendible state and the standard maximally entangled state. Our findings, coupled with the resource theory of $k$-unextendibility, lead to an efficiently computable upper bound on the one-shot, one-way distillable key of a bipartite state, and we prove that it is equal to the best-known efficiently computable upper bound on the one-shot, one-way distillable entanglement. We also establish efficiently computable upper bounds on the one-shot, forward-assisted private capacity of channels. Extending our formalism to the independent and identically distributed setting, we obtain single-letter efficiently computable bounds on the $n$-shot, one-way distillable key of a state and the $n$-shot, forward-assisted private capacity of a channel. For some key examples of interest, our bounds are significantly tighter than other known efficiently computable bounds.

Problem

• Determining maximum probability k-extendible states pass privacy tests
• Establishing computable bounds on one-way distillable secret key
• Providing tighter bounds for quantum channel private capacities

Innovation

• Using privacy tests and extendible states
• Establishing fidelity-based bounds for secure communication
• Providing computable bounds for distillable key rates