[Paper Review] Noise as a resource

Stefano Gherardini|arXiv (Cornell University)|May 4, 2018

Advanced Thermodynamics and Statistical Mechanics202 references3 citations

TL;DR

This PhD thesis proposes a resource theory of noise, demonstrating that stochastic interactions with an environment can be harnessed to enhance state estimation, quantum transport efficiency, and quantum measurement protocols. By modeling noise as a controllable parameter via large deviation theory and stochastic estimation, the work shows that noise can optimize system response, enable noise-robust sensing, and reveal non-equilibrium thermodynamic features such as entropy production and quantum Zeno dynamics.

ABSTRACT

In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of specific control tasks, since it can be responsible for uncontrolled time-dependent changes of the system. However, if the effects of the random interaction with a noisy environment are properly modeled by the introduction of a given stochasticity within the dynamics of the system, then even noise contributions might be seen as control knobs. As a matter of fact, even a partial knowledge of the environment can allow to set the system in a dynamical condition in which the response is optimized by the presence of noise sources. In particular, we have investigated what kind of measurement devices can work better in noisy dynamical regimes and studied how to maximize the resultant information via the adoption of estimation algorithms. Moreover, we have shown the optimal interplay between quantum dynamics, environmental noise and complex network topology in maximizing the energy transport efficiency. Then, foundational scientific aspects, such as the occurrence of an ergodic property for the system-environment interaction modes of a randomly perturbed quantum system or the characterization of the stochastic quantum Zeno phenomena, have been analyzed by using the predictions of the large deviation theory. Finally, the energy cost in maintaining the system in the non-equilibrium regime due to the presence of the environment is evaluated by reconstructing the corresponding thermodynamics entropy production. In conclusion, the present thesis can constitute the basis for an effective resource theory of noise, which is given by properly engineering the interaction between a dynamical system and its external environment.

Motivation & Objective

• To reframe environmental noise from a detrimental factor to a controllable resource in dynamical systems.
• To develop estimation frameworks that exploit noise for improved state reconstruction using binary sensors and stochastic measurements.
• To optimize energy transport in quantum networks by engineering noise and network topology.
• To analyze foundational quantum phenomena—such as stochastic quantum Zeno effects and ergodicity—using large deviation theory.
• To quantify thermodynamic costs of non-equilibrium dynamics via stochastic projective measurements and entropy production.

Proposed method

• Formulates a unified framework integrating open quantum systems, statistical estimation, and statistical mechanics.
• Applies large deviation theory to analyze survival probabilities and stochastic quantum Zeno effects in repeated measurements.
• Develops moving horizon estimation (MHE) and maximum a-posteriori (MAP) filtering for binary sensor data with constraints.
• Introduces a fast MH-MAP filter for large-scale systems using sequential sampling and approximation techniques.
• Employs stochastic projective measurement protocols to derive quantum heat statistics and fluctuation theorems.
• Uses characteristic functions and spectral decompositions to compute Fisher information and entropy production in stochastic quantum processes.

Experimental results

Research questions

• RQ1 Can noise be systematically engineered to improve state estimation accuracy in noisy dynamical systems?
• RQ2 How does stochasticity in measurement sequences affect the emergence of quantum Zeno dynamics?
• RQ3 What is the role of environmental noise in enhancing energy transport efficiency in complex quantum networks?
• RQ4 Can the stochastic quantum Zeno effect be observed and characterized using large deviation theory?
• RQ5 How is thermodynamic irreversibility quantified through stochastic entropy production in non-equilibrium quantum systems?

Key findings

• Noise can be harnessed as a control knob: optimal noise levels enhance state estimation accuracy and energy transport efficiency.
• The stochastic quantum Zeno effect is analytically characterized via large deviation theory, showing suppression of system evolution under frequent stochastic measurements.
• A fast MH-MAP filter enables efficient state estimation in large-scale systems with binary sensors, achieving stability and convergence.
• Noise correlations in measurement sequences can be detected using Fisher information, enabling noise-robust quantum sensing.
• Quantum heat transfer is induced by stochastic waiting times in projective measurements, with fluctuation theorems confirmed in the model.
• Ergodicity of system-environment interaction modes is demonstrated in randomly perturbed quantum systems, supporting statistical predictability.