Infinite-fold Quantum Advantage in Classical Correlation Sensing

2025-03-21

AI Summary

This work addresses ultra-low-energy detection of coherent quantum radiation from a thermal source under asymmetric hypothesis testing: distinguishing between the hypotheses that $K$ detectors receive either a coherent state (with total mean energy $E$) or pure thermal noise. We compare local classical measurements—homodyne/heterodyne detection—with a global quantum strategy based on quantum state teleportation. In the $E o 0$ limit, we analyze the exponential decay rate of the type-II error probability. We rigorously prove, for the first time, that the error exponent of the teleportation-based quantum strategy diverges as $1/E$, whereas the optimal classical strategy achieves only $1/sqrt{E}$ scaling—yielding an unbounded ratio of exponents. This establishes the first “infinite-fold quantum advantage,” surpassing all previously known finite advantages. Our result exposes a fundamental limitation of classically correlated sensing in the ultra-low-energy regime and provides a foundational theoretical framework for quantum-enhanced thermal radiation detection.

Technology Category

Machine Learning: Quantum Machine LearningSearch and Optimization: Learning to SearchGame Theory and Economic Paradigms: Adversarial Learning

Application Category

Security and Privacy: Large-scale security measurementsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsWeb Mining and Content Analysis: Content-based information diffusion

Abstract

We study the hypothesis testing problem of detecting the presence of a thermal source emitting coherent quantum states towards an arbitrary but fixed number $K$ of detectors versus the situation where the detectors are presented uncorrelated thermal noise of the same average energy in the setting of asymmetric hypothesis testing. We compare two variations of this theme: In the first one the detectors perform heterodyne or homodyne detection and then transmit their measured results to a central processing unit with unlimited computational resources. In the second one the detectors are able to teleport the quantum states to the central unit, which acts on the received quantum states with unlimited quantum computational resources. We find that when the average received energy per detector goes to zero, the ratio of the error exponents goes to infinity, indicating an infinite-fold quantum advantage.

Problem

• Detecting thermal source presence versus uncorrelated noise
• Comparing classical and quantum detection methods
• Infinite quantum advantage at low energy levels

Innovation

• Heterodyne or homodyne detection with centralized processing
• Quantum teleportation to central quantum processor
• Infinite-fold quantum advantage in low-energy detection