Comparing physical quantities with finite-precision: beyond standard metrology and an illustration for cooling in quantum processes

TL;DR

This paper introduces a universal framework for comparing physical quantities with finite precision, using percentiles instead of standard deviation, and demonstrates its application in quantum cooling processes.

Contribution

It develops a general method for comparing physical quantities with finite precision, extending beyond standard metrological approaches, and applies it to quantum cooling in a three-qubit system.

Findings

Finite-precision cooling occurs in quantum refrigerators.

Cooling is demonstrated in both transient and steady states.

The approach works across different coupling regimes.

Abstract

We propose a general framework to compare the values of a physical quantity pertaining to two - or more - physical setups, in the finite-precision scenario. Such a situation requires us to compare between two "patches" on the real line instead of two numbers. Identification of extent of the patches is typically done via standard deviation, as obtained within usual quantum metrological considerations, but can not be always applied, especially for asymmetric error distributions. The extent can however be universally determined by utilizing the concept of percentiles of the probability distribution of the corresponding estimator. As an application, we introduce the concept of finite-precision cooling in a generic quantum system. We use this approach in the working of a three-qubit quantum refrigerator governed by Markovian dynamics, and demonstrate the occurrence of cooling within finite precision for both transient and steady-state regimes, across strong- and weak-coupling limits of the inter-qubit interaction.