Thermodynamical properties of quantum systems have been the object of study from many recent papers. In this dissertation, we begin with a brief review of quantum thermodynamics papers, where we focus on the rst law. We show that there are many different denitions of work and heat on quantum systems. We focus on one of the most usual denitions andwe present a recent work from Augusto Roncaglia et al. [1]. On this paper, they propose a method to measure the variation of the internal energy of a quantum system between two instants of time with a single measure by making the system interact with an ancilla twice. This method will be used as a starting point for this dissertation. We will explain how totransform the measurement protocol into one that continuously monitors a system and we will describe some conditions that the system must obey to make this monitoring possible. We show how the ancilla, which will also serve as the measurement apparatus, work and we will dene a quality factor for the measures. At last, we will study a specic system and will show how to use the protocol to obtain the time-dependance of an unknown hamiltonian. In order to do this, we use an algorithm that simulates the measurements proposed here and show that the protocol can not only effectively reconstruct the unknown hamiltonian but also obtain the total work and heat exchanged between the system and a reservoir.
Thermodynamical properties of quantum systems have been the object of study from many recent papers. In this dissertation, we begin with a brief review of quantum thermodynamics papers, where we focus on the rst law. We show that there are many different denitions of work and heat on quantum systems. We focus on one of the most usual denitions andwe present a recent work from Augusto Roncaglia et al. [1]. On this paper, they propose a method to measure the variation of the internal energy of a quantum system between two instants of time with a single measure by making the system interact with an ancilla twice. This method will be used as a starting point for this dissertation. We will explain how totransform the measurement protocol into one that continuously monitors a system and we will describe some conditions that the system must obey to make this monitoring possible. We show how the ancilla, which will also serve as the measurement apparatus, work and we will dene a quality factor for the measures. At last, we will study a specic system and will show how to use the protocol to obtain the time-dependance of an unknown hamiltonian. In order to do this, we use an algorithm that simulates the measurements proposed here and show that the protocol can not only effectively reconstruct the unknown hamiltonian but also obtain the total work and heat exchanged between the system and a reservoir.
We propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system's dynamics, but not all of it, one can use the measured energy to determine many other quantities, such as the work performed on the system, the heat exchanged between the system and a thermal reservoir, the time dependence of the Hamiltonian of the system as well as the total entropy produced by its dynamics. We have also analyzed how this method is dependent on the quality factor of the measurements employed.
During the last decades, there have been many theoretical and experimental advances both in the extension of thermodynamics to comprise microscopic systems out-of-equilibrium and in the understanding of quantum mechanics. Along with the state-of-the-art capability of controlling fragile quantum systems in a wide variety of physical platforms, this context has paved the way for the current strategic efforts to develop a thermodynamic theory of quantum systems. In this sense, the research field coined as quantum thermodynamics (QT) already plays a key role in the design and development of future quantum-based technologies. More specifically, QT aims both to apply the usual thermodynamic concepts and notions to describe arbitrary non-equilibrium quantum systems and to understand the emergence of classical thermodynamic behaviour from the underlying fundamentally quantum dynamics. However, despite all current progress, there is still no consolidated formalism for a general thermodynamic description of fully autonomous quantum objects. Besides, the lack of consensus on some central aspects, such as the definitions of quantum counterparts of thermodynamic quantities, is particularly notorious. In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt decomposition approach, we identify effective Hamiltonians as the representative operators for characterizing the local internal energies, whose expectation values satisfy the usual thermodynamic notion of energy additivity. In contrast to the currently used methodologies, such procedure treats the subsystems with equal footing and do not rely on any sort of approximations and additional hypotheses, e.g., semi-classical description, weak-coupling regime, strict energy conservation and Markovian dynamics. In short, our proposal contributes to the development of QT by providing a new formalism that does not suffer from the usual restrictive shortcomings and establishes a new and exact route for defining other general thermodynamic quantities to the quantum regime.
Para sistemas quânticos fechados, a energia é uma observável que pode ser representada por uma matriz hermitiana chamada de hamiltoniano. Com a hamiltoniano que descreve o sistema quântico, podemos determinar a sua dinâmica através da equação de Schrödinger, que diz a taxa de variação de um estado |ψ(t)⟩ com respeito a um determinado instante t. Resolvendo a equação para um estado inicial consegue-se determinar a evolução do sistema. Utilizando o hamiltoniano que descreve um sistema de duplos pontos quânticos, e medindo as observáveis locais, aplicamos o modelo de aprendizado de máquina Extra-Trees com o objetivo de realizar a tomografia completa do hamiltoniano. Ficou demonstrado a efetividade da solução em diversas situações e, afim de obter diretrizes para auxiliar o físico experimental, realizamos analises exploratórias com o intuito de melhorar o entendimento sobre o problema de tomografia de hamiltoniano.
The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Here, we provide an introduction to the general theoretical framework to establish and interpret the thermodynamics for quantum systems whose nonequilibrium evolution is continuously monitored. We review the formalism of quantum trajectories and its consistent application to the thermodynamic scenario, where primary quantities such as work, heat, and entropy production can be defined at the stochastic level. The connection to irreversibility and fluctuation theorems is also discussed together with some recent developments, and we provide some simple examples to illustrate the general theoretical framework.
According to the axioms of quantum mechanics, there exists a quantum measurement corresponding to each observable.Energy is one of such observables, and the operator of the energy is called Hamiltonian.The Hamiltonian specifies the dynamics of closed quantum systems and it also characterizes the property of the equilibrium state in contact with a heat bath.Therefore the energy is an essential quantity in quantum mechanics, which characterizes behavior of a quantum system.On the other hand, since the Hamiltonian is not a local observable in general, a concrete construction of how to apply the quantum measurement of energy is not trivial.Thus various measurement models of energies have been proposed, and also discussions have been made on whether the time is a resource to be consumed to increase the precision of energy measurement in connection with the time-energy uncertainty relationship.Constructing a way to implement the energy measurement on an unknown Hamiltonian system is important, since it avoids constructing a new measurement scheme for each new quantum system.On the other hand, among measurements of energy, the projective measurement of energy has useful properties for applications.The projective measurement is a measurement which satisfies the condition so-called repeatable hypothesis that when we measure the state immediately after obtaining an outcome from the same measurement, we obtain the same outcome again.In this thesis, we consider two schemes to implement the projective measurement of energy for an unknown Hamiltonian system.One is a tomography based method, which is a construction suggested in the paper of Aharanov et.al. (2002).The other is the phase estimation based method, which utilizes the Hamiltonian dynamics of the system as a resource for the quantum algorithm, and realizes the projective measurement of energy on the system without identifying all parameters of the Hamiltonian.In this thesis, we assume there is a finite dimensional quantum system (quantum computer) which is able to apply any interaction between the target system and the finite dimensional system although the interaction should not depend on the target system Hamiltonian.To evaluate the performance of the measurements implemented by the two schemes, we formulate two evaluation functions called fluctuation of measurement value and non-repeatability, which can evaluate how much a measurement is different from the ideal projective measurement of an observable.We calculate a sufficient time to guarantee the fluctuation of measurement value below some small value ε, for each of the two measurement schemes.We find that the tomography based method takes the time proportional to O(d 4 ∆ max /ε), while the phase estimation based method takes O(∆ 3 max /ε 2 ), where d is the dimension of the target system and ∆ max is the difference between the largest energy eigenvalue and the smallest energy eigenvalue.We show that the phase estimation based method performs better for large particle systems.
In the last two decades there has been an increasing interest for the quantum estimation theory.Among various research topics there's a recent eort to better understand quantum estimation for open quantum systems, which are known to have worse precision than the closed systems.Our work focused on open quantum systems where we explored out of equilibrium thermometry.To do this we used a single q-bit model in contact with a thermal reservoir and changed it's dynamic by adding two distinct eects: rst we added a stochastic eld, which can maintain the system out of equilibrium for longer periods, using two types of noises; on the second case we used a time-dependent frequency for the q-bit which generates a protective eect against decoherence also extending the period in which the system is out of equilibrium.In both cases we studied how these secondary eects aected the precision of temperature estimations for the reservoir temperature, using data extracted from the q-bit which becomes equivalent to a thermometer.For the stochastic eld we found out that it's possible to achieve higher precision for low temperatures in which the eects of the eld prevail.For the time-dependent frequency we couldn't nd any evidence for a better precision but the delay on the eects of decoherence allows for more time to estimate the temperature, which may oer some advantages for experimental measurements.