Enhancing the performance of quantum switch refrigeration with an information pool of qubits

Indefinite causal order has been shown to enable nonclassical refrigeration, with recent experimental verification using an ensemble of nuclear spins in the nuclear magnetic resonance system that boosted prior coefficient of performance (COP) through the approach of density matrix exponentiation (DME). In this paper, we demonstrate an approach to improve the COP of this setup by incorporating an information pool of qubits to absorb the entropic cost of refrigeration. If these qubits are reused until their resources are expended, an increase of the COP beyond the DME approach can be achieved in certain temperature ranges. This improvement is found to hold even for the case when the working body is hotter than the cold bath, and in the prethermalization regimes where further enhancements can be observed. Our work thus introduces a technique to enhance quantum refrigeration with indefinite causal order.