Measurement-based qudit quantum refrigerator with subspace cooling

TL;DR

This paper introduces a measurement-based protocol called subspace cooling to transform high-temperature thermal states of spin systems into low-energy eigenstates, demonstrating high fidelity and robustness against decoherence in certain configurations.

Contribution

The paper presents a novel subspace cooling method using auxiliary systems and projective measurements, applicable to higher-dimensional spin systems, with analysis of its effectiveness and limitations.

Findings

Unit fidelity achieved with repeated measurements in open chain configurations.

Success probability increases with measurement projector rank.

Method remains effective even with some subsystems in thermal contact, showing resistance to decoherence.

Abstract

We develop a method to transform a collection of higher-dimensional spin systems from the thermal state with a very high temperature of a local spin-s Hamiltonian to a low-lying energy eigenstate of the same. The procedure utilizes an auxiliary system, interactions between all systems, and appropriate projective measurements of arbitrary rank performed on the auxiliary system. We refer to this process as subspace cooling. The performance of the protocol is assessed by determining the fidelity of the target state with the output one and the success probability of achieving the resulting state. For this analysis, spin-s XXZ and bilinear biquadratic models are employed as the evolving Hamiltonian. We demonstrate that in both scenarios, unit fidelity can be attained after a reasonable number of repeated measurements and a finite amount of evolution time when all the systems are aligned in an open chain, but it fails when the interactions between the spin follow the star configuration. We report that the success probability increases with the rank of the projectors in the measurement for a fixed dimension and that for each dimension, there exists a range of interaction strength and evolution period for which the fidelity gets maximized. Even when some subsystems are in contact with the thermal bath, the method proves to be resistant to decoherence.