Refrigeration limits are of fundamental and practical importance. We here show that quantum systems can be cooled below existing incoherent cooling bounds by employing coherent virtual qubits, even if the amount of coherence is incompletely known. Virtual subsystems, that do not necessarily correspond to a natural eigensubspace of a system, are a key conceptual tool in quantum information science and quantum thermodynamics. We derive universal coherent cooling limits and introduce specific protocols to reach them. As an illustration, we propose a generalized algorithmic cooling protocol that outperforms its current incoherent counterpart. Our results provide a general framework to investigate the performance of coherent refrigeration processes.
Refrigeration limits are of fundamental and practical importance. We here show that quantum systems can be cooled below existing incoherent cooling bounds by employing coherent virtual qubits, even if the amount of coherence is incompletely known. Virtual subsystems, that do not necessarily correspond to a natural eigensubspace of a system, are a key conceptual tool in quantum information science and quantum thermodynamics. We derive universal coherent cooling limits and introduce specific protocols to reach them. As an illustration, we propose a generalized algorithmic cooling protocol that outperforms its current incoherent counterpart. Our results provide a general framework to investigate the performance of coherent refrigeration processes.
The theory of cooling is an important corner of thermodynamics, underlying many modern technological applications.As the field of quantum thermodynamics advances, refrigeration techniques must keep pace to fuel the innovations of quantum technologies.We study quantum cooling from its foundations to laboratory implementations within the specific paradigm of heat bath algorithmic cooling.Our study includes a detail modeling of experimental imperfections and establishes the fundamental cooling limits of the model, consolidating the algorithm as a viable quantum refrigeration method.Next, by developing the notion of virtual qubits, we demonstrate a cooling-boost protocol fueled by quantum coherences which is robust to experimental implementations.Aiming at aiding in the progress of refrigeration technologies, we conclude by studying the zero temperature equilibrium properties of a many-body system that can accommodate an autonomous quantum absorption refrigerator, and calculate its entanglement and critical properties, two features that, like quantum coherences, promise to improve the performance of quantum coolers.
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.
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. Evaluating this contribution is an important but non-trivial problem. Here, focusing on quantum refrigeration, we show how the level of control determines the fundamental limits to cooling. We compare coherent versus incoherent operations, and derive the minimal achievable temperature and associated work cost. We discuss both the single-shot and asymptotic regimes. 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.
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.
This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined. The connection that these paradigms have with other existing refrigeration techniques such as heat bath algorithmic cooling (HBAC), the resource theoretic approach to quantum thermodynamics, and autonomous cooling is then made. Each paradigm is then investigated on its own. This in particular allows for the derivation of a general and attainable bound. The bound is striking in its simplicity: it depends on a single parameter of the environment/machine used to cool the system of interest. The creation of correlations part is devoted to the quantitative study of how much correlations can be created for a given amount of energy. After having precisely formulated the problem of interest, we solve it for arbitrary finite dimensional bipartite systems for vanishing background temperatures. For non-vanishing background temperature the symmetry of the problem breaks down, making it much harder to tackle. When both systems are copies of each other, enough symmetry is restored to formulate an upper bound valid for all (finite) dimensional systems and prove its attainability for dimension 3 and 4. We furthermore conjecture, as well as show evidence for, the bound to be attainable in any dimension.
Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, however, have attracted a great deal of attention in the past few years. In this paper, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a tradeoff relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called "bounding second order cooling rate" and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second-order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second-order cooling rate. We study the efficiency of the refrigerator at maximum bounding second-order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second-order cooling rate is given by a simple formula resembling the Curzon-Ahlborn relation.