# Fundamental Relations between Measurement, Radiation and Decoherence in Gravitational Wave Laser Interferometer Detectors

## TL;DR

This paper derives fundamental quantum limits for gravitational wave detectors by calculating the quantum Fisher information, revealing how measurement sensitivity, radiation, and decoherence are interconnected through quantum uncertainty principles.

## Contribution

It provides explicit reciprocity relations linking quantum Fisher information, radiation, and decoherence in GW detectors, advancing understanding of quantum measurement limits.

## Key findings

- Quantum Fisher information relates to GW radiation power.
- Decoherence rate is inversely proportional to quantum Fisher information.
- Fundamental quantum limits are derived for GW detection sensitivity.

## Abstract

As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection -- specifically the quantum Cramer Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state's quantum Fisher information (QFI) with respect to the parameter. Identifying the QFI requires knowing the interaction between the quantum measurement device and the signal, which was rigorously derived for GW interferometer detectors in [Phys. Rev. D 98, 124006]. In this paper, we calculate the QFI and fundamental quantum limit (FQL) for GW detection, and furthermore derive explicit reciprocity relations involving the QFI which summarize information exchange between the detector and a surrounding weak quantum GW field. Specifically, we show that the GW power radiation by the detector's quantum fluctuations are proportional to the QFI, and therefore inversely proportional to its FQL. Similarly, the detector's decoherence rate in a white noise GW bath can be explicitly related to the QFI/FQL. These relations are fundamental and appear generalizable to a broader class of quantum measurement systems.