Neste dissertação apresentamos um protocolo para simular, no contexto das armadilhas iônicas, o Zitterbewegung não usual, que é o análogo, na física do semicondutores, ao movimento de tremulação de uma partícula relativística. O Zitterbewegung não usual permite trajetórias cicloidais na ausência dos campos magnéticos. Além do Zitterbewegung, mostramos como gerar figuras de Lissajou para o movimento vibracional bidimensional do íon armadilhado. Ademais, o protocolo proposto nesta tese, permite gerar interações spin-órbita dos tipos Rashba e Dresselhaus, abrindo a possibilidade de simular, no âmbito dos íons armadilhados, os acoplamentos spin-órbita dos tipos Rashba e Dresselhaus, Zitterbewegung não usual e as curvas de Lissajou. Além disso, nesta tese apresentamos protocolo para produzir engenharia de interações confinadas aos subespaços do espaço de Fock. Mostramos como engenheirar os hamitonianos dos tipos Jaynes-Cumming e anti-Jaynes-Cumming confinadados aos subespaços de Fock delimitados superiormente ou inferiormente e também as interações Jaynes-Cumming e anti-Jaynes-Cumming confinados a uma fatia do espaço Fock. Esses hamitonias delimitados superiormente (inferiormente) atuam sobre os subespaço de Fock de |0&rang; a |M&rang; (|N&rang; &alpha;&infin;), enquanto aqueles confinados a uma fatia do espaço de Fock atuam sobre os subespaço de Fock de |M&rang; a |N&rang; com M < N. Enquanto que, as interações dos tipo Jaynes-Cumming ou anti-Jaynes-Cumming demilitadas superiormente conduzem qualquer estado inicial para o estado de Fock de quase-equilíbrio |N&rang; e as interações confinadas a uma fatia do espaço de Fock conduz qualquer estado inicial a superporsição de estados de Fock de equilíbrio, que estão confinados no subespaço {|N&rang; , |N + 1&rang;}. / In this dissertation we present a protocol to simulate, with a single two-leve trapped ion, the unusual zitterbewegung: the semiconductor analog of the relativistic trembling motion of eletron, allowing cycloidal trajectories in the absence of magnetic fields. Beyon zitterbewegung, we show how to generate Lissajou curves from the vibrational motion of an ion in two dimensional trap. Morever our protocol enables us to engineerthe Rashbaand the Dresselhaus-type spin-orbit interatiction, opening the possibility to simulate with a trapped ion, spin-orbit effects other than the unusual zitterbewegung and Lissajou curves. Moreover, in this work we present a protocol to engineer interactions confined to subspaces of the Fock space: we show how to engineer upper-, lower-bounded and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upperbounded (lower-bounded) interaction acting upon Fock subspaces ranging from |0&rang; to |M&rang; (|N&rang; to &infin;), and the sliced one confined to Fock subspace ranging from |M&rang; to |N&rang;, whatever M < N. Whereas the upper-bounded JC or AJC interactions is shown to drive any initial state to an equilibrium Fock states |N&rang;, the sliced one is shown to produce equilibrium superpositions of Fock states confined to the sliced subspaces {|N&rang; , |N + 1&rang;}.

Neste dissertação apresentamos um protocolo para simular, no contexto das armadilhas iônicas, o Zitterbewegung não usual, que é o análogo, na física do semicondutores, ao movimento de tremulação de uma partícula relativística. O Zitterbewegung não usual permite trajetórias cicloidais na ausência dos campos magnéticos. Além do Zitterbewegung, mostramos como gerar figuras de Lissajou para o movimento vibracional bidimensional do íon armadilhado. Ademais, o protocolo proposto nesta tese, permite gerar interações spin-órbita dos tipos Rashba e Dresselhaus, abrindo a possibilidade de simular, no âmbito dos íons armadilhados, os acoplamentos spin-órbita dos tipos Rashba e Dresselhaus, Zitterbewegung não usual e as curvas de Lissajou. Além disso, nesta tese apresentamos protocolo para produzir engenharia de interações confinadas aos subespaços do espaço de Fock. Mostramos como engenheirar os hamitonianos dos tipos Jaynes-Cumming e anti-Jaynes-Cumming confinadados aos subespaços de Fock delimitados superiormente ou inferiormente e também as interações Jaynes-Cumming e anti-Jaynes-Cumming confinados a uma fatia do espaço Fock. Esses hamitonias delimitados superiormente (inferiormente) atuam sobre os subespaço de Fock de |0&rang; a |M&rang; (|N&rang; &alpha;&infin;), enquanto aqueles confinados a uma fatia do espaço de Fock atuam sobre os subespaço de Fock de |M&rang; a |N&rang; com M < N. Enquanto que, as interações dos tipo Jaynes-Cumming ou anti-Jaynes-Cumming demilitadas superiormente conduzem qualquer estado inicial para o estado de Fock de quase-equilíbrio |N&rang; e as interações confinadas a uma fatia do espaço de Fock conduz qualquer estado inicial a superporsição de estados de Fock de equilíbrio, que estão confinados no subespaço {|N&rang; , |N + 1&rang;}. / In this dissertation we present a protocol to simulate, with a single two-leve trapped ion, the unusual zitterbewegung: the semiconductor analog of the relativistic trembling motion of eletron, allowing cycloidal trajectories in the absence of magnetic fields. Beyon zitterbewegung, we show how to generate Lissajou curves from the vibrational motion of an ion in two dimensional trap. Morever our protocol enables us to engineerthe Rashbaand the Dresselhaus-type spin-orbit interatiction, opening the possibility to simulate with a trapped ion, spin-orbit effects other than the unusual zitterbewegung and Lissajou curves. Moreover, in this work we present a protocol to engineer interactions confined to subspaces of the Fock space: we show how to engineer upper-, lower-bounded and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upperbounded (lower-bounded) interaction acting upon Fock subspaces ranging from |0&rang; to |M&rang; (|N&rang; to &infin;), and the sliced one confined to Fock subspace ranging from |M&rang; to |N&rang;, whatever M < N. Whereas the upper-bounded JC or AJC interactions is shown to drive any initial state to an equilibrium Fock states |N&rang;, the sliced one is shown to produce equilibrium superpositions of Fock states confined to the sliced subspaces {|N&rang; , |N + 1&rang;}.

Foundational problems of quantum theory, regarding the appearance of classicality and the measurement problem are stated and their link to studies of open quantum systems is discussed. This study&#039 / s main aim is to analyze the main approaches that are employed in the context of open quantum systems. The general form of Markovian master equations are derived by a constructive approach. The Quantum State Diffusion (QSD) formalism is stressed upon as an alternative method to the master equations. Using the Caldeira-Leggett model in the context of QSD, stationary solutions of a charged particle exposed to a uniform magnetic field are found. The important points are summarized and the results are discussed.

The scattering of H2 from Si(100) has been studied using pulsed molecular beam techniques and quantum state-specific detection methods. These studies can be used to test theoretical calculations and give insight into new theories of molecule-surface interactions, a fundamental study in a diverse field of science and technology. In this work, time-of-flight (TOF) spectra of the elastic scattering of H2(v=1. J=1) and H2(v=0, J=1) from clean Si were recorded over a wide range of surface temperatures. Two data processing strategies were developed to extract rich kinematic information from the scattering experiments, e.g., mean translational energy exchange, absolutely survival probability, and angular and speed distribution of the scattered molecules. No such set of quantitative results has been reported before for this system. Compared with close packed metal surfaces, these scattering experiments from a covalently bonded semiconductor surface showed a completely distinct dynamics, e.g. the finding of energy gain instead of loss from the substrate, much broader angular distribution and some counterintuitive surface temperature effects. From the studies of molecules/surface scattering experiments, the thermal excitation on Si(100) surface which depends on surface temperature can substantially alter the adsorption barrier and its distribution, and therefore changes the kinematics of scattered molecules. As a result, even the most basic understanding of the dynamics has to include phonon excitation and deexcitation of the silicon substrate. / text

xii, 133 p. : ill. (some col.) / We study entanglement estimation and verification in realistic situations, taking into account experimental imperfections and statistical fluctuations due to finite data. We consider both photonic and spin-1/2 systems. We study how entanglement created with mixed photon wave packets is degraded. We apply statistical analysis to and propose criteria for reliable entanglement verification and estimation. Finally we devote some effort to making quantum state estimation efficient by applying information criteria. This dissertation includes previously published co-authored material. / Committee in charge: Michael G. Raymer, Chair; Steven J. van Enk, Advisor; Stephen Hs,u Member; Jens U. Noeckel, Member; Je rey A. Cina, Outside Member;

Orientador: Marcos César de Oliveira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin. / Made available in DSpace on 2018-08-13T03:07:21Z (GMT). No. of bitstreams: 1 Steinhoff_FrankEduardodaSilva_M.pdf: 633661 bytes, checksum: 4c5305fba85a1d80713ed5dfe1f90f32 (MD5) Previous issue date: 2009 / Resumo: Propomos um método para obtenção de propriedades de sistemas quânticos compostos utilizando apenas medições estritamente locais e comunicação clássica. Isso difere dos esquemas usualmente utilizados em protocolos de informação quântica, que se utilizam em sua maioria de operações globais e/ou operações locais conjuntas. Nosso tratamento consiste em analisar o efeito de medições em um subsistema sobre as submatrizes da matriz densidade do sistema composto. Analisamos então como outros subsistemas podem ser expressos em termos dessas submatrizes, obtendo assim o efeito das medições feitas em um subsistema sobre os outros. Aplicamos esse resultado - válido para sistemas com espaços de Hilbert discretos de dimensão arbitrária - a dois problemas centrais em protocolos de informação quântica: a reconstrução de estados de sistemas compostos e a caracterização de emaranhamento. Para a tarefa de reconstrução, mostramos como determinar um estado de um sistema composto de dimensão finita arbitrária utilizando apenas medições locais e comunicação clássica de uma via. A vantagem de nossa proposta está em eliminar a necessidade de medições conjuntas, o que se traduz, no contexto de ótica linear, em eliminar medições de coincidência. Analisamos a caracterização de emaranhamento considerando classes especiais de estados. Para estados com alta simetria - estados isotrópicos, de Werner e de simetria rotacional constituídos por um qubit e um qudit - mostramos uma relação entre o grau de emaranhamento e a diferença de população medida por um subsistema condicionada a medições de paridade do outro subsistema, relação essa já evidenciada em estados gaussianos simétricos. Além disso, propomos uma nova família de estados cujo emaranhamento pode ser caracterizado com muito menos recursos do que os utilizados para a reconstrução, sendo esses recursos estritamente locais. / Abstract: We propose a method to obtain properties of composite quantum systems using strictly local measurements and classical communication only. This differs from schemes usually employed in quantum information protocols where global and/or joint local operations are commonly used. Our treatment consists of analysing the effect of measurements of a system over submatrices of the density matrix of the compound system. We analyse then how copies of a subsystem can be expressed in terms of these submatrices, obtaining thus the effect of the measurements done in a subsystem upon the others. We apply this result - valid for discrete Hilbert spaces of arbitrary dimension - to two central problems in quantum information protocols: the state reconstruction of composite systems and entanglement characterization. For the reconstruction task, we show how to determine a state of a arbitrary finite dimension composite system using local measurements and one-way classical communnication only. The advantage of our proposal lies in elimnating the need for joint measurements, which translates as eliminating coincidence measurements in linear optics context. We analyse entanglement characterization considering special classes of states. For high symmetry states -isotropic states, Werner states and rotationally symmetric states composed of a qubit and a qudit - we show a relation between entanglement degree and population difference measured by one subsystem conditioned to parity measurements of the other subsystem, this relation already present in gaussian symmetric states. Moreover, we propose a new family os states whose entanglement can be characterized with much fewer resources than that used for reconstruction, this resources being strictly local. / Mestrado / Física / Mestre em Física

Orientadores: Carlile Campos Lavor, Wilson Ricardo Matos Rabelo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T05:05:06Z (GMT). No. of bitstreams: 1 Evangelista_TatianedaSilva_D.pdf: 1204224 bytes, checksum: 78ba86ca8ac235e2775ed6a048ccf353 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho, apresentamos um novo algoritmo para realizar a discriminação ótima de N estados quânticos puros não-ortogonais, que fornece o melhor conjunto de medidas POVM para o problema, através da extensão do espaço de Hilbert de N para 2N - 1 dimensões. O algoritmo é baseado na programação semidefinida e na solução de sistemas lineares. O algoritmo foi implementado em Matlab e apresentou bons resultados computacionais. / Abstract: In this work, we propose a new algorithm to perform the optimal discrimination of N non-orthogonal pure quantum states. This algorithm obtains the best set of POVM measurements for the problem, through the extension of the Hilbert space of N to 2N-1 dimensions. The algorithm is based on semidefinite programming and on the solution of linear systems. The algorithm was implemented in Matlab and presented good computational results. / Doutorado / Otimização / Doutor em Matemática Aplicada

<p dir="ltr">This thesis advances the methodologies of quantum state tomography (QST) to validate and optimize quantum processing on Noisy Intermediate-Scale Quantum (NISQ) devices, crucial for the transition to practical quantum systems. Inspired by recent advancements in the field, we propose a novel QST method based on the maximal entropy formalism, specifically addressing scenarios with incomplete measurement sets to provide a robust framework for state reconstruction. We extend this formalism to an informationally complete (IC) set of observables and introduce a variational approach for quantum state preparation, easily implementable on near-term quantum devices. Our developed maximal entropy-based QST protocol is applied to ultrafast molecular dynamics specifically for studying photoexcited ammonia molecule, enabling direct measurement and manipulation of electronic quantum coherences and exploring entanglement effects in molecular systems. Through this approach, we achieve a groundbreaking milestone by, for the first time, constructing the entanglement entropy of the electronic subsystem - an otherwise inaccessible metric. In doing so it also provides the first physical interpretation of the maximal entropy parameters in an experimental setting and highlights the potential for feedback between time-resolved quantum dynamics and quantum information science. Furthermore, building upon our advancements in state tomography, we propose a variational quantum algorithm for Hamiltonian learning that leverages the time dynamics of observables. Additionally, we reverse engineer the maximal entropy approach and demonstrate the use of entropy to refine the traditional geometric Brownian motion (GBM) method for better capturing real system complexities by addressing its log-normality restrictions, which opens new avenues for quantum sampling techniques. Through these contributions, this thesis showcases the Maximal Entropy formalism’s efficacy in QST and set the stage for future innovations and applications in cutting-edge quantum research.</p>

Issues of control and causation are central to the Quantum Theory of Computation. Yet there is no place for them in fundamental laws of Physics when expressed in the prevailing conception, i.e., in terms of initial conditions and laws of motion. This thesis aims at arguing that Constructor Theory, recently proposed by David Deutsch to generalise the quantum theory of computation, is a candidate to provide a theory of control and causation within Physics. To this end, I shall present a physical theory of information that is formulated solely in constructor-theoretic terms, i.e., in terms of which transformations of physical systems are possible and which are impossible. This theory solves the circularity at the foundations of existing information theory; it provides a unifying relation between classical and quantum information, revealing the single property underlying the most distinctive phenomena associated with the latter: the unpredictability of the outcomes of some deterministic processes, the lack of distinguishability of some states, the irreducible perturbation caused by measurement and the existence of locally inaccessible information in composite systems (entanglement). This thesis also aims to investigate the restrictions that quantum theory imposes on copying-like tasks. To this end, I will propose a unifying, picture-independent formulation of the no-cloning theorem. I will also discuss a protocol to accomplish the closely related task of transferring perfectly a quantum state along a spin chain, in the presence of systematic errors. Furthermore, I will address the problem of whether self-replication (as it occurs in living organisms) is compatible with Quantum Mechanics. Some physicists, notably Wigner, have argued that this logic is in fact forbidden by Quantum Mechanics, thus claiming that the latter is not a universal theory. I shall prove that those claims are invalid and that the logic of self-replication is, of course, compatible with Quantum Mechanics.

This thesis is concerned with the collective dynamics in different spin chains and spin ensembles in solid-state materials. The focus is on the manipulation of electron spins, through spin-spin and spin-photon couplings controlled by voltage potentials or electromagnetic fields. A brief review of various systems is provided to describe the possible physical implementation of the ideas, and also outlines the basis of the adopted effective interaction models. The first two ideas presented explore the collective behaviour of non-interacting spin chains with external couplings. One focuses on mapping the identical state of spin-singlet pairs in two currents onto two distant, static spins downstream, creating distributed entanglement that may be accessed. The other studies a quantum memory consisting of an array of non-interacting, static spins, which may encode and decode multiple flying spins. Both chains could effectively `enhance' weak couplings in a cumulative fashion, and neither scheme requires active quantum control. Moreover, the distributed entanglement generated can offer larger separation between the qubits than more conventional protocols that only exploit the tunnelling effects between quantum dots. The quantum memory can also `smooth' the statistical fluctuations in the effects of local errors when the stored information is spread. Next, an interacting chain of static spins with nearest-neighbour interactions is introduced to connect distant end spins. Previously, it has been shown that this approach provides a cubic speed-up when compared with the direct coupling between the target spins. The practicality of this scheme is investigated by analysing realistic error effects via numerical simulations, and from that perspective relaxation of the nearest-neighbour assumption is proposed. Finally, a non-interacting electron spin ensemble is reviewed as a quantum memory to store single photons from an on-chip stripline cavity. It is then promoted to a full quantum processor, with major error effects analysed.