ULSAN — Researchers have established a theoretical criterion that clearly distinguishes changes in the microscopic quantum world driven by simple heat exchange alone from processes that additionally require hidden external energy resources. The framework is expected to serve as a core foundational theory for calculating the energy costs and efficiency limits of next-generation quantum technologies such as quantum computers and nanodevices.
Lee Seok-hyung, a professor in the Department of Physics at Ulsan National Institute of Science and Technology (UNIST), said on Sept. 22 that his team, working with international collaborators from Nanyang Technological University in Singapore, Freie Universität Berlin and Leibniz University Hannover in Germany, has presented a mathematical criterion that separates purely "thermal operations" from general "quantum thermal processes," based on the concept of "informational equilibrium." The findings were published in Physical Review Letters, the most prestigious journal in the field of physics.
Unlike macroscopic thermodynamic systems, which are described by average statistical values such as temperature and pressure, microscopic quantum systems require precise analysis of changes in individual energy states at the level of atoms or qubits. In conventional quantum thermodynamics, "Gibbs-preserving maps," which keep a system in thermal equilibrium, have been widely used. But they had a limitation in that they could not clearly determine whether hidden non-equilibrium resources in the surrounding environment were being consumed during actual implementation.
The team solved this problem by taking as its starting point the condition of "informational equilibrium," under which two independent quantum systems each retain their own intrinsic states even after undergoing an interaction that preserves information. Through mathematical proof, the researchers demonstrated that only processes capable of simultaneously preserving the equilibrium state of the surrounding environment when a quantum system is in thermal equilibrium qualify as purely "thermal operations." Conversely, they established that Gibbs-preserving maps that appear to maintain the state of a quantum system but do not belong to thermal operations inevitably alter the environment and must consume separate non-equilibrium resources.
Extending this principle, the team also proved the physical limits of "quantum catalysts," which help change the state of a quantum system while returning to their original state. The researchers mathematically confirmed that when error-tolerant catalysts, which are unaffected by minute errors in the initial state, are used, adding more catalysts cannot expand the scope of purely thermal operations.
"This study is meaningful in that it derived the principles of thermal operations from an informational condition — that the states of a quantum system and its surrounding environment are preserved — without predetermining the temperature or the energy of each quantum state," Lee said.
Lee added: "To assess the resources and costs required to operate quantum computers, nanodevices and quantum heat engines, we must distinguish quantum processes that are possible solely by exchanging heat with the surrounding environment from those that require additional resources. By presenting the criterion for that distinction, this study can be used as a foundational theory for analyzing the energy costs of quantum information processing devices and the performance limits of quantum heat engines."
The study was conducted jointly with Professor Nelly Ng of Nanyang Technological University, researcher Son Jeong-rak of Freie Universität Berlin, Professor Henrik Wilming of Leibniz University Hannover and independent researcher Paul Boes. The research was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) under the Ministry of Science and ICT and the National Research Foundation of Korea.
