Finite-frequency fluctuation-response bounds for open quantum systems

TL;DR

This paper establishes a finite-frequency fluctuation-response inequality for open quantum systems, linking measurable responses to quantum Fisher information and channel activity, with applications to various quantum optical setups.

Contribution

It introduces a new finite-frequency fluctuation-response bound for open quantum systems that is measurement-agnostic and applies to multiple channels and quadratures.

Findings

The response-to-noise matrix is bounded by the quantum Fisher information rate.

For vacuum inputs, the information rate is bounded by a frequency-independent signal-channel activity.

The bounds are demonstrated on systems like cavity resonance fluorescence and Kerr resonators.

Abstract

We derive a finite-frequency fluctuation-response inequality for Markovian open quantum systems in an input-output setting. For any downstream measurement of the emitted field, the measured lock-in response-to-noise matrix is bounded by the output-field quantum Fisher information rate. For dissipative amplitude modulation with vacuum inputs, this information rate is further bounded by a frequency-independent signal-channel activity, which reduces for kinetic modulation to the stationary channel fluxes. The result is detector-facing but unraveling-independent: it applies after choosing a measurement record, while the information ceiling is set by the quantum field before any detection scheme or trajectory representation is selected. We formulate the bound for multiple signal channels and real finite-frequency quadratures, and illustrate it with a single-sided cavity, resonance fluorescence, and a truncated Kerr-parametric cat resonator.