Abstract
Quantum channels inevitably degrade coherence and thereby reshape the precision scaling predicted by ideal Heisenberg limits. Rather than attributing this reduction to probe choice, measurement strategy, or architectural details, we present a compact, channel-centric framework in which the impact of noise is captured by a single coherence function governing an L-fold coherent interrogation. Within this formulation, the channel alone determines both how long ideal Heisenberg scaling can be sustained and where precision saturation must occur. The commonly observed “knee” in noisy-metrology precision curves emerges as a direct and unavoidable consequence of the competition between coherent phase amplification and channel-induced loss of state distinguishability. By isolating channel effects into a retention function, we introduce simple, dimensionless metrics that quantify (i) the fraction of ideal Heisenberg performance that survives noise and (ii) the remaining advantage over the standard quantum limit. This perspective yields a universal and platformindependent design principle: precision is limited not by how deeply one attempts to interrogate coherently, but by how rapidly the channel erases the information that deeper interrogation seeks to amplify.
Research Context
This paper is part of CSA's quantum research program connecting quantum metrology, structured environmental noise, decoherence, quantum communication, and operationally relevant quantum-system engineering.
Citation
@misc{sidhu2026quantumchannelprecisionreductionlaw,
author = {Deepinder Sidhu},
title = {Precision Reduction in Quantum Channels: A Universal Channel Law},
year = {2026},
note = {CyberSpace Analytics Quantum Research Series}
}