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.
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.
Abstract Correlations lie at the heart of almost all scientific predictions. It is therefore of interest to ask whether there exist general limitations to the amount of correlations that can be created at a finite amount of invested energy. Within quantum thermodynamics such limitations can be derived from first principles. In particular, it can be shown that establishing correlations between initially uncorrelated systems in a thermal background has an energetic cost. This cost, which depends on the system dimension and the details of the energy-level structure, can be bounded from below but whether these bounds are achievable is an open question. Here, we put forward a framework for studying the process of optimally correlating identical (thermal) quantum systems. The framework is based on decompositions into subspaces that each support only states with diagonal (classical) marginals. Using methods from stochastic majorisation theory, we show that the creation of correlations at minimal energy cost is possible for all pairs of three- and four-dimensional quantum systems. For higher dimensions we provide sufficient conditions for the existence of such optimally correlating operations, which we conjecture to exist in all dimensions.
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 study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.
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.
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.
The field of quantum information has inspired new methods for cooling physical systems at the quantum scale by manipulating entropy in an algorithmic way, such as heat-bath algorithmic cooling (HBAC). These methods not only provide fundamental insight into quantum thermodynamics, but they are also at the core of practical applications in quantum science and quantum technologies. Arguably, the most promising practical applications are in quantum computing, for the preparation of pure states. The ability to prepare highly pure states is required both for initializing qubits in most quantum algorithms and for supplying reliable low-noise ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction (achieving the high levels of purity required represents one of the major challenges not only for ensemble implementations but also for technologies with strong but not perfect projective measurements). \n \n \nThe heat bath algorithmic cooling protocols have inspired the work within this thesis, which examines and proposes powerful new techniques that significantly enhance cooling by taking advantage of classical and quantum correlations. These new methods go beyond the limits of conventional cooling techniques, providing a novel way to cool that allows a generalized interaction of the system with the environment, which has not been taken into account in previous work. Concretely, I have contributed to elucidating our understanding of these algorithmic cooling mechanisms by using techniques from quantum information theory and quantum thermodynamics. First, I found the analytical solution of the maximum achievable cooling of these algorithmic cooling methods, which had been a longstanding problem that remained open for almost 15 years. Then, I showed how to circumvent the cooling limits of the conventional algorithmic cooling – which were widely believed to be optimal –, creating novel methods that show how correlations can be used to significantly improve cooling. On the one hand, we fundamentally changed the way previous methods considered the interactions between the system and environment and showed how correlated relaxation processes can be essential for enhancing cooling. On the other hand, we demonstrated that correlations present in the initial state due to internal interactions can be exploited to improve cooling. Finally, we showed how, by using ideas and concepts from resource theory, it is possible to find the optimal entropy compression required for HBAC by studying the n-to-1 distillation of athermality of two level systems.