Resource engines

Hanna Wojewódka-Ściążko1,2, Zbigniew Puchała2, and Kamil Korzekwa3

1Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007 Katowice, Poland
2Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland
3Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland

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In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based predominantly on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two–stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.

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[1] Kohdai Kuroiwa, Ryuji Takagi, Gerardo Adesso, and Hayata Yamasaki, "Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories", Physical Review A 109 4, 042403 (2024).

[2] Kohdai Kuroiwa, Ryuji Takagi, Gerardo Adesso, and Hayata Yamasaki, "Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity", Physical Review Letters 132 15, 150201 (2024).

[3] Gökhan Torun, Onur Pusuluk, and Özgür E. Müstecaplıoğlu, "A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics", arXiv:2306.11513, (2023).

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