In this paper we argue that one-way quantum computation can be seen as a form of phase transition with the available information about the solution of the computation being the order parameter. We draw a number of striking analogies between standard thermodynamical quantities such as energy, temperature, work, and corresponding computational quantities such as the amount of entanglement, time, potential capacity for computation, respectively. Aside from being intuitively pleasing, this picture allows us to make novel conjectures, such as an estimate of the necessary critical time to finish a computation and a proposal of suitable architectures for universal one-way computation in 1D.
We consider a generalisation of thermodynamics that deals with multiple conserved quantities at the level of individual quantum systems. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike in standard thermodynamics, where the second law places a constraint on how much of the conserved quantity (energy) that can be extracted, here, on the contrary, there is no limit on how much of any individual conserved quantity that can be extracted. However, other conserved quantities must be supplied, and the second law constr…
The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between …
Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? We give a strong argument that justifies uncertainty relations…
Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics, information science and biology. Recently, it has been realised that information storage and processing based on quantum mechanics can be much more efficient than their classical counterpart. What general bound on storage of quantum information does thermodynamics imply? We show that thermodynamics implies a weaker bound than the quantum mechanical one (the Hol…
We analyze the lowest achievable temperature for a mechanical oscillator (representing, for example, the motion of a single trapped ion) which is coupled with a driven quantum refrigerator. The refrigerator is composed of a parametrically driven system (which we also consider to be a single oscillator in the simplest case) which is coupled to a reservoir where the energy is dumped. We show that the cooling of the oscillator (that can be achieved due to the resonant transport of its phonon excitations into the environment) is always stopped by a fundamental heating process that is always domina…
In the previous companion paper, we proposed a subclass of wavefunctions to describe macroscopic solids that resolved and extended the theory quantum measurement and gave a more specific treatment of quasiparticles. Here we extend these notions to thermalization of solids and gases and to gas state hydrodynamics. This gives a modification of the thermodynamic limit to justify the canonical averages for "typical wavefunctions" without the use of ensembles. The energetic cost of vorticity is contrasted in the classical and ultracold gas limits. From this perspective, we then examine the applicab…
We explore the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems (TLS), alias qubits, in contact with a thermal bath. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control of heating, cooling and state-purification (entropy reduction) of qubits, much sooner than their thermal equilibration time.
We present a thermodynamic framework for the refined weak coupling limit. In this limit the interaction between system and environment is weak, but not negligible. As a result, the system dynamics becomes non-Markovian breaking divisibility conditions. Nevertheless, we propose a derivation of the first and second law just in terms of the reduced system dynamics. To this end, we extend the refined weak coupling limit for allowing slowly-varying external drivings, and reconsider the definition of internal energy due to the non-negligible interaction.
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…
We study the functioning of a three-level thermal machine when acting on a many-qubit system, the entire system being placed in an electromagnetic field in a stationary out-of-thermal-equilibrium configuration. This realistic setup stands in between the two so-far explored cases of single-qubit and macroscopic object targets, providing information on the scaling with system size of purely quantum properties in thermodynamic contexts. We show that, thanks to the presence of robust correlations among the qubits induced by the field, thermodynamic tasks can be delivered by the machine both locall…
For a two-level quantum mechanical system, we derive microscopically the exact expression for the fluctuation of microscopic work in a multi-step non-equilibrium process, and we rigorously prove that in an isothermal process, the fluctuation is vanishingly small, and the most probabilistic work just equals to the difference of the free energy. Our study demonstrates that the convergence of the microscopic work in the isothermal process is due to the nature of isothermal process rather than usual thermodynamic limit condition. Our investigation justifies the validity of "minimum work principle"…
For the ideal Fermi gas that fills a quantum well confined by two parallel planes, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. The distance between planes is considered as an additional thermodynamic variable. Owing to the anisotropy, the pressure of the Fermi gas along and transverse to the planes is different, so that the system is characterized by two equations of state and a set of different heat capacities. Limiting cases o…
Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intra-relaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time i…
Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of quantum thermodynamics allows for catalysts, i.e., systems facilitating state transformations while remaining essentially intact in their state, very much reminding of catalysts in chemical reactions. In this work, we present a comprehensive analysis of the power and limitation of such thermal catalysis. Specifically, we provide a family of optimal catalysts that can be returned with minimal trace distance error after facilitating…
In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix product states (MPSs) in the limit of infinite system size. We obtain a lower bound to the GE which collapses to an equality under certain sufficient conditions that are fulfilled by many physical systems, such as those having unbroken space (P) or space-time (PT) inversion symmetry. Our analysis justifies the validity of several derivations carried out in previou…
A 1D Josephson junction loop, doped with a spin-flipper and attached to two thermal reservoirs, operates as a heat engine or a refrigerator, a Joule pump, or even a cold pump. When operating as a quantum heat engine, the efficiency of this device exceeds that of some recent Josephson heat engine proposals. Further, as a quantum refrigerator, the coefficient of performance of this device is much higher than previously proposed Josephson junction-based refrigerators. In addition, this device can be tuned from engine mode to refrigerator mode or any other mode, i.e., Joule pump or cold pump, by e…
