Abstract We investigate catalysis in the framework of elementary thermal operations (ETOs), leveraging the distinct features of such operations to illuminate catalytic dynamics. As groundwork, we establish new technical tools that enhance the computability of state transition rules for ETOs. Specifically, we provide a complete characterisation of state transitions for a qutrit system and special classes of initial states of arbitrary dimension. By employing these tools in conjunction with numerical methods, we find that by adopting a small catalyst, including just a qubit catalyst, one can significantly enlarge the set of state transitions for a qutrit system. This advancement notably narrows the gap of reachable states between ETOs and generic thermal operations. Furthermore, we decompose catalytic transitions into time-resolved evolution, which critically enables the tracking of nonequilibrium free energy exchanges between the system and bath. Our results provide evidence for the existence of simple and practicable catalytic advantage in thermodynamics while offering insight into analysing the mechanism of catalytic processes.
Abstract We investigate catalysis in the framework of elementary thermal operations (ETOs), leveraging the distinct features of such operations to illuminate catalytic dynamics. As groundwork, we establish new technical tools that enhance the computability of state transition rules for ETOs. Specifically, we provide a complete characterisation of state transitions for a qutrit system and special classes of initial states of arbitrary dimension. By employing these tools in conjunction with numerical methods, we find that by adopting a small catalyst, including just a qubit catalyst, one can significantly enlarge the set of state transitions for a qutrit system. This advancement notably narrows the gap of reachable states between ETOs and generic thermal operations. Furthermore, we decompose catalytic transitions into time-resolved evolution, which critically enables the tracking of nonequilibrium free energy exchanges between the system and bath. Our results provide evidence for the existence of simple and practicable catalytic advantage in thermodynamics while offering insight into analysing the mechanism of catalytic processes.
Thermal operations are a generic description for allowed state transitions under thermodynamic restrictions. However, the quest for simpler methods to encompass all these processes remains unfulfilled. We resolve this challenge through the catalytic use of thermal baths, which are assumed to be easily accessible. We select two sets of simplified operations: elementary thermal operations and Markovian thermal operations. They are known for their experimental feasibility, but fail to capture the full extent of thermal operations due to their innate Markovianity. We nevertheless demonstrate that this limitation can be overcome when the operations are enhanced by ambient-temperature Gibbs state catalysts. In essence, our result indicates that free states within thermal operations can act as catalysts that provide the necessary non-Markovianity for simpler operations. Furthermore, we prove that when any catalyst can be employed, different thermal processes (thermal operations, elementary thermal operations, and Markovian thermal operations) converge. Notably, our results extend to scenarios involving initial states with coherence in the energy eigenbasis, a notoriously difficult process to characterise.
Abstract Thermal operations (TO) are a generic description for allowed state transitions under thermodynamic restrictions. However, the quest for simpler methods to encompass all these processes remains unfulfilled. We resolve this challenge through the catalytic use of thermal baths, which are assumed to be easily accessible. We select two sets of simplified operations: elementary TO (ETO) and Markovian TO (MTO). They are known for their experimental feasibility, but fail to capture the full extent of TO due to their innate Markovianity. We nevertheless demonstrate that this limitation can be overcome when the operations are enhanced by ambient-temperature Gibbs state catalysts. In essence, our result indicates that free states within TO can act as catalysts that provide the necessary non-Markovianity for simpler operations. Furthermore, we prove that when any catalyst can be employed, different thermal processes (TO, ETO, and MTO) converge. Notably, our results extend to scenarios involving initial states with coherence in the energy eigenbasis, a notoriously difficult process to characterise.
What are the fundamental limits and advantages of using a catalyst to aid thermodynamic transformations between quantum systems? In this paper, we answer this question by focusing on transformations between energy-incoherent states under the most general energy-conserving interactions among the system, the catalyst, and a thermal environment. The sole constraint is that the catalyst must return unperturbed and uncorrelated with the other subsystems. More precisely, we first upper bound the set of states to which a given initial state can thermodynamically evolve (the catalyzable future) or from which it can evolve (the catalyzable past) with the help of a strict catalyst. Secondly, we derive lower bounds on the dimensionality required for the existence of catalysts under thermal process, along with bounds on the catalyst's state preparation. Finally, we quantify the catalytic advantage in terms of the volume of the catalyzable future and demonstrate its utility in an exemplary task of generating entanglement and cooling a quantum system using thermal resources. Published by the American Physical Society 2024
Quantum thermodynamics is a blossoming research program that uses tools and ideas from quantum information theory to extend the laws of thermodynamics to the domain of systems to which the laws of quantum mechanics apply and the thermodynamic limit does not necessarily apply. The contributions of this program are both foundational, in providing an approach to constructively derive the laws of phenomenological thermodynamics from the postulates of unitary quantum mechanics in a rigorous and bottom-up fashion, but also prac- tical, in providing the theory for an increasing number of experiments that attempt to build thermodynamic machines at scales that were previously inaccessible. One key mathematical tool used in quantum thermodynamics is the framework of resource theories, specifically the resource theory of thermal operations, in which the thermodynamic interaction of a system with a heat bath and various additional components such as work batteries, clocks or catalysts are modeled. In this cumulative thesis, various extensions and modifications of this framework are studied in order to derive novel results and insights about the possible thermodynamic evolution of quantum systems. In particular, following a system- atic exposition of the resource theory of thermal operations from first principles, I develop answers to the following questions: i) What is the smallest heat bath required to provide the necessary randomness for a system to undergo a given stochastic or thermodynamical evolution? ii) Does this size differ depending on whether the interaction between bath and system is quantum or classical? iii) How can quantum systems thermodynamically evolve in the presence of catalytic bystander systems and how can this be put to use? iv) What are the thermodynamic state transitions that an agent can operationally affect when she only has access to partial information about the underlying states of system and bath? v) How can we understand the emergence of the canonical ensemble in statistical thermodynamics from quantum mechanics? These questions cover a wide ground, but it will become clear that they can in fact all be discussed using the same formal tools. As such, the answers to the above questions provided in this thesis are both interesting in their own right — showing for example that there exists a gap in how efficiently randomness can be exploited quantumly as compared to classically or that catalytic bystander systems can be used to extract finite amounts of work per particle from macroscopic systems with non-vanishing probability — as well as illustrate the power of quantum thermodynamics as a set of tools to connect quantum mechanics and the theory of thermodynamics more generally.
Quantum catalysis, the ability to enable previously impossible transformations by using auxiliary systems without degrading them, has emerged as a powerful tool in various resource theories. Although catalytically enabled state transformations have been formally characterized by the monotonic behavior of entropic quantifiers (e.g., the von Neumann entropy or nonequilibrium free energy), such characterizations often rely on unphysical assumptions, namely, the ability of using catalysts of infinitely large dimension. This approach offers very limited insights into the practical significance of using catalysis for quantum information processing. Here, we address this problem across a broad class of quantum resource theories. Leveraging quantum information tools beyond the asymptotic regime, we establish sufficient conditions for the existence of catalytic transformations with finite-size catalysts. We further unveil connections between finite-size catalysis and multicopy transformations. Notably, we discover a phenomenon of catalytic resonance: by carefully tailoring the catalysts's state, one can drastically reduce the required dimension of the catalyst, thus enabling efficient catalytic transformations with minimal resources. Finally, we illustrate our findings with examples from the resource theories of entanglement and thermodynamics, as well in the context of catalytic unitary transformations.
In quantum information and computation, a central challenge is to determine which quantum states can be transformed into which others under restricted sets of free operations. While many transformations are impossible directly, catalytic processes can enable otherwise forbidden conversions: an auxiliary quantum state (the catalyst) facilitates the transformation while remaining unchanged. In this work, we introduce flexible catalysis, a generalization in which the catalyst is allowed to transform into a different auxiliary state, provided it remains a valid catalyst. We show that this framework subsumes both standard catalytic and multicopy transformations, and we analyse its advantages across several classes of free operations. In particular, we prove that when the free operations are local unitaries or permutation matrices, flexible catalysis enables state extractions that are unattainable with standard catalysis alone.