The preparation of quantum states, especially cooling, is a fundamental technology for nanoscale devices. The past decade has seen important results related to both the limits of state transformation and the limits to their efficiency -- the quantum versions of the third and second law of thermodynamics. The limiting cases always involve an infinite resource cost, typically machine complexity or time. Realistic state preparation takes into account both a finite size of the machine and constraints on the operations we can perform. In this work, we determine in full generality the optimal operation for a predominant quantum paradigm: state transformation under a single unitary operation upon a finite system, in the case where the observables corresponding to the target (such as ground state probability) and cost (such as dissipation) commute. We then extend this result to the case of having a third, commuting, globally conserved quantity (such as total energy). The results are demonstrated with the paradigmatic example of ground state cooling, for both arbitrary and energy-preserving unitary operations.
The preparation of quantum states, especially cooling, is a fundamental technology for nanoscale devices. The past decade has seen important results related to both the limits of state transformation and the limits to their efficiency -- the quantum versions of the third and second law of thermodynamics. The limiting cases always involve an infinite resource cost, typically machine complexity or time. Realistic state preparation takes into account both a finite size of the machine and constraints on the operations we can perform. In this work, we determine in full generality the optimal operation for a predominant quantum paradigm: state transformation under a single unitary operation upon a finite system, in the case where the observables corresponding to the target (such as ground state probability) and cost (such as dissipation) commute. We then extend this result to the case of having a third, commuting, globally conserved quantity (such as total energy). The results are demonstrated with the paradigmatic example of ground state cooling, for both arbitrary and energy-preserving unitary operations.
Landauer's limit on heat dissipation during information erasure is critical as devices shrink, requiring optimal pure-state preparation to minimize errors. However, Nernst's third law states this demands infinite resources in energy, time, or control complexity. We address the challenge of cooling quantum systems with finite resources. Using Markovian collision models, we explore resource trade-offs and present efficient cooling protocols (that are optimal for qubits) for coherent and incoherent control. Leveraging thermodynamic length, we derive bounds on heat dissipation for swap-based strategies and discuss the limitations of preparing pure states efficiently.
In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.
The laws of thermodynamics are usually formulated under the assumption of infinitely large environments. While this idealization facilitates theoretical treatments, real physical systems are always finite and their interaction range is limited. These constraints have consequences for important tasks such as cooling, not directly captured by the second law of thermodynamics. Here, we study catalytic transformations that cannot be achieved when a system exclusively interacts with a finite environment. Our core result consists of constructive conditions for these transformations, which include the corresponding global unitary operation and the explicit states of all the systems involved. From this result we present various findings regarding the use of catalysts for cooling. First, we show that catalytic cooling is always possible if the dimension of the catalyst is sufficiently large. In particular, the cooling of a qubit using a hot qubit can be maximized with a catalyst as small as a three-level system. We also identify catalytic enhancements for tasks whose implementation is possible without a catalyst. For example, we find that in a multiqubit setup catalytic cooling based on a three-body interaction outperforms standard (non-catalytic) cooling using higher order interactions. Another advantage is illustrated in a thermometry scenario, where a qubit is employed to probe the temperature of the environment. In this case, we show that a catalyst allows to surpass the optimal temperature estimation attained only with the probe.
Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this Letter we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.
Thermodynamics is one of the main pillars of theoretical physics, and it has a special appeal of having wide applicability to a large variety of different physical systems. However, many assumptions in thermodynamics apply only to systems which are bulk material, i.e. consisting a large number of microscopic classical particles. Due to the advancement of designing nanoscale engines, especially in the light of devices that are used today in the processing of quantum information, is thermodynamics still applicable? Can we refine the core principles of thermodynamics to suit such nanoscale quantum systems as well? The central aim of this thesis is to construct a theory of thermodynamics that holds for nanoscale quantum systems, even those as small and simple as a single qubit. We do this by starting out from the core basics of quantum theory: unitary dynamics on closed quantum systems. We adapt a resource theoretic approach inspired by quantum information theory, which defines the quantum states and operations allowed to be used in a thermodynamic evolution. With this framework that naturally adopts the first law as an energy preserving condition, we show the refinement of both the zeroeth and second law of thermodynamics. The zeroeth law explains the physical significance of the Gibbs thermal state. On the other hand, we show that the second law sees refinement in the quantum nanoregime: instead of having the free energy as the sole quantity dictating the possibility of a thermodynamic state transition, we derive a family of generalized free energies that also constitute necessary conditions for a transition to occur. Moreover, these conditions become sufficient for states which are block-diagonal in the energy eigenbasis. In this thesis, we also brought our approach of thermodynamics to the next step: we apply our findings on the second laws, in order to analyze the maximum achievable efficiency for quantum heat engines. In classical thermodynamics, the Carnot efficiency has been long known as the theoretical maximum which does not depend on the specific structure of the thermal baths used, but only on its temperature. With the additional free energies we discover, we show that although quantum heat engines may achieve the Carnot efficiency, such an achievability is no longer independent of the Hamiltonians of the thermal baths. In other words, we find additional restrictions that surface in the study of quantum nanoscale heat engines, which are a direct consequence of the generalized second laws. This has provided us with a deeper understanding into the fundamental limitations of how efficient devices can be made in the realm of microscopic quantum systems.
We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian. In a general context, we show that this model can exactly implement any energy-conserving unitary on the engine, without degrading the clock. Furthermore, we show that when the engine includes a quantum work storage device we can approximately perform completely general unitaries on the remainder of the engine. This framework can be used in quantum thermodynamics to carry out arbitrary transformations of a system, with accuracy and extracted work as close to optimal as desired, while obeying the first and second laws of thermodynamics. We thus show that autonomous thermal machines suffer no intrinsic thermodynamic cost compared to externally controlled ones.