Enhancing precision thermometry with nonlinear qubits

TL;DR

This paper demonstrates that nonlinear qubits can significantly improve the precision of quantum thermometry by increasing quantum Fisher information, especially in simple single and two-qubit systems.

Contribution

It introduces the use of nonlinear Schrödinger equations to enhance quantum thermometry precision, a novel approach compared to traditional linear models.

Findings

Nonlinear qubits yield larger quantum Fisher information.

Thermal Gibbs states are not invariant under nonlinear dynamics.

Enhanced precision is linked to non-vanishing quantum speed limits.

Abstract

Quantum thermometry refers to the study of measuring ultra-low temperatures in quantum systems. The precision of such a quantum thermometer is limited by the degree to which temperature can be estimated by quantum measurements. More precisely, the maximal precision is given by the inverse of the quantum Fisher information. In the present analysis, we show that quantum thermometers that are described by nonlinear Schr\"odinger equations allow for a significantly enhanced precision, that means larger quantum Fisher information. This is demonstrated for a variety of pedagogical scenarios consisting of single and two-qubits systems. The enhancement in precision is indicated by non-vanishing quantum speed limits, which originate in the fact that the thermal, Gibbs state is typically not invariant under the nonlinear equations of motion.