Private Correlations Certify Sensing Capability

Quantum sensing aims to estimate parameters with precision exceeding classical limits, but noise often degrades the sensing state's performance. This paper investigates whether operational information-theoretic quantities—specifically private correlations—can certify a nontrivial lower bound on the sensing capability of a noisy quantum state, effectively bridging the gap between quantum communication resources and metrological performance.

The authors analyze distributed sensing protocols where Alice and Bob share a bipartite state. They consider a scenario where Alice holds a parameter-encoded system and an additional subsystem. By transmitting the parameter-independent subsystem to Bob through a noisy assisting channel, Bob can perform joint measurements to recover sensing information. The researchers utilize the concept of private information—the ability to distill a secret key—to derive a quantitative lower bound on the locally accessible Fisher information, which characterizes the precision of parameter estimation.

The study establishes that positive private information in the encoding basis certifies a strictly positive lower bound on the locally accessible Fisher information after assistance. The authors demonstrate this through a data-hiding state example, showing that while the state has poor sensing performance initially, assistance significantly improves it even under high noise. They prove a general theorem showing that this privacy-based guarantee is robust and distinct from classical correlations, which fail to provide similar guarantees. Furthermore, they show that in the absence of the assisting subsystem, this privacy-based guarantee reduces to one based on entanglement, highlighting the role of privacy as a more noise-robust resource.

This work provides a new paradigm for noisy distributed sensing, showing that information-theoretic properties can be translated into rigorous metrological guarantees. By identifying that privacy can certify sensing capability, the authors offer a framework for utilizing states that may lack distillable entanglement but still possess useful private correlations, potentially expanding the class of states suitable for high-precision quantum sensing protocols.