9 June 2022 Thu 11 am

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Catalysts are auxiliary states that interact with the system of interest during a process, and recover their original state afterwards. The benefit of appending such an ancilla has been reported in many frameworks, including quantum thermodynamics. Nevertheless, current results focus mainly on conditions for catalytic advantage. In contrast, the dynamics of catalytic processes have remained unexplored. Moreover, the existing state transition conditions relying on initial and final states, washes out what happens in a continuous-time setting, preventing us from gleaning insight into the potential mechanisms that make a catalyst useful. Motivated by the status quo, we study catalysis in elementary thermal operations (ETO), an experimentally motivated subset of thermal operations, and show that catalysis enhances ETO, which was previously unknown. The structure of ETOs furthermore allow us to trace intermediate steps of the evolution, enabling a study on how system and catalyst explicitly interact with each other. A critical tool we develop is the strengthening of existing upper bounds of computational cost for ETOs, which leads to 1) a full characterization of the three-dimensional system transitions, and 2) computationally tractable numerics for higher dimensions. Interestingly, non-trivial catalyses with exact recovery are found even in the simplest case of a qutrit system and qubit catalyst, fostering experimental implementation together with straightforward operational recipes provided by ETO. Finally, we capture “snapshots” of the catalysis at work, by tracking local free energies of the system-catalyst during evolution. We observed that the system free energy, which always decrease after each ETO, can increase momentarily during the catalytic processes by borrowing catalyst free energies. Our work provides the first analysis of catalysis mechanism occurring in practicable setup, paving the way for a more in-depth understanding of catalytic processes.

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