Since the beginning of the 20th century, much time and effort has been invested in the search for a theory of quantum gravity. While this provided a myriad of possibilities, it has so far failed to find a definitive answer. Here we take an alternative approach: instead of constructing a theory of quantum gravity and examining its low energy limit, we start with the conventional theory and ask what are the first deviations induced by a possible quantization of gravity. It is proposed that in this limit quantum gravity, whatever the ultimate theory might be, manifests itself as non-locality. In this thesis are explored two different approaches to effective theories. In the first, it is demonstrated how combining quantum field theory with general relativity naturally gives rise to non-locality. This is explored in the context of inflation, a natural place to look for high energy phenomena. By considering a simple scalar field theory, it is shown how non-locality results in higher dimensional operators and what the effects are on inflationary models. The second approach looks at a theory which naturally incorporates a minimal scale. Noncommutative geometry parallels the phase space or deformation quantization approach of quantum mechanics. It supposes that at short scales, the structure of spacetime is algebraic rather than geometric. In the first instance, we follow the first section and look at cosmological implications by replacing normal scalar theory with its noncommutative counterpart. In the second, we take a step back and examine the implications of quantization on the differential geometry. The formalism is developed and applied to generic spherically symmetric spacetimes where it is shown that to first order in deformation, the quantization is unique.

Decoherence and errors appear among the main challenges to implement successful quantum technologies. In this thesis I discuss the application of some general tools and principles that may be valuable resources to develop robust technologies, with applications in quantum sensing and quantum simulation. Firstly, we employ suitable periodically driving fields acting on the Ising model in order to tailor spin-spin interactions depending on the spatial direction of the bonds. In this way, we are able to simulate the quantum compass model on a square lattice. This system exhibits topological order and a doubly degenerate ground state protected against local noise. A possible implementation of this proposal is outlined for atomic quantum simulators. Secondly, we exploit two general working principles based on spontaneous symmetry breaking and criticality that may be beneficial to achieve robust quantum sensors, particularly appropriate for quantum optical dissipative systems. A concrete application is given for a minimal model: a single qubit laser. It is shown how the precision in parameter estimation is enhanced as the incoherent pumping acting on the qubit increases, and also when the system is close to the lasing critical point. Finally, classical long-range correlations in lattice systems are shown to provide us with an additional resource to be used in robust sensing schemes. The previous setup is extended to a lattice of single qubit lasers where interactions are incoherent. Under the right conditions, we show that a Heisenberg scaling with the number of probes can be accomplished.

No presente trabalho usamos técnicas de física de muitos corpos não relativísticas para generalizar o limite clássico de sistemas quânticos de forma a incorporar misturas estatísticas. Efeitos de temperatura finita são estudados em detalhe no contexto das versões integrável e não integrável do modelo de Lipkin-Meshkov-Glick. Os dois aspectos mais notáveis de nossa análise são: o surgimento de um novo grau de liberdade essencialmente conectado a efeitos térmicos, ocorrendo a temperaturas suficientemente altas e uma caracterização quantitativa do efeito da temperatura no volume caótico do sistema. Mostra-se que os efeitos térmicos sistematicamente compensam a parte de interação da dinâmica. Este é o caso tanto no contexto da termodinâmica quanto da dinâmica a temperatura finita e acreditamos que seja verdadeiro em geral. / In the present work we use techniques of nonrelativistic many body physics to generalize the classic limit of quantum systems in such a way as to incorporate statistical mixtures. Finite temperature effects are studied in detail in the context of the integrable and nonintegrable versions of the Lipkin-Meshkov-Glick Model. The most remarkable features of our analysis is twofold: the appearance of a new degree of freedom essentially connected to thermal effects i.e., for high enough temperatures and a quantitative characterization of the temperature on the chaotic volume of the system. Thermal effects can be shown to consistently counterbalance the interaction part of the dynamics. This is the case both in the context of thermodynamics and of the thermal dynamics of the system and we believe it to be true in general.

It has been almost eighty years since quantum mechanics emerged as a complete theory, yet debates about how should quantum mechanics be interpreted still occur. Interpretations are many and varied, some taking us as fundamental in determining reality (orthodox interpretation), while others proposing that reality exists outside of us, but it is a lot more complicated than that implied by classical mechanics. In this thesis I am going to try to provide new light on this debate by investigating dynamics under both the orthodox and modal interpretation. In particular I will answer the question what is the interpretation of non-Markovian stochastic Schrodinger equations? I conclude that under the orthodox view these equations have only a numerical interpretation. They provide a rule for calculating the state of the system at time t if we made a measurement on the bath (a collection of oscillators {ak}) at that time, yielding results {zk}. However in the modal view they have a meaning: non-Markovian stochastic Schrodinger equations represent the evolution of the system part of the property state of the universe (bath + system).

This thesis is concerned with retrodiction and measurement in quantum optics. The latter of these two concepts is studied in particular form with a general optical multiport device, consisting of an arbitrary array of beam-splitters and phase-shifters. I show how such an apparatus generalizes the original projection synthesis technique, introduced as an in principle technique to measure the canonical phase distribution. Just as for the original projection synthesis, it is found that such a generalised device can synthesize any general projection onto a state in a finite dimensional Hilbert space. One of the important findings of this thesis is that, unlike the original projection synthesis technique, the general apparatus described here only requires a classical, that is a coherent, reference field at the input of the device. Such an apparatus lends itself much more readily to practical implementation and would find applications in measurement and predictive state engineering. If we relax the above condition to allow for just a single non-classical reference field, we show that the apparatus is capable of producing a single-shot measure of canonical phase. That is, the apparatus can project onto any one of an arbitrarily large subset of phase eigenstates, with a probability proportional to the overlap of the phase state and the input field. Unlike the original projection synthesis proposal, this proposal requires a binomial reference state as opposed to a reciprocal binomial state. We find that such a reference state can be obtained, to an excellent approximation, from a suitably squeezed state. The analysis of these measurement apparatuses is performed in the less usual, but completely rigorous, retrodictive formalism of quantum mechanics.

<p>This Master  thesis considers certain aspects of Supersymmetric Quantum Mechanics in the context of Path integral approach. First we state all the basic mathematical structure involved, and carry out some basic Gaussian integrals for both commutative and non-commutative variables. Later in the thesis these simple results obtained are generalized to study the Supersymmetric sigma models on flat and curved space. And we will recover the beautiful relationship between the supersymmetric sigma  model and the geometry of the  target manifold in the form of topological invariants of the manifold, for the models on curved space.</p>

Arising out of the EPR debate, the Bell and Wigner inequalities of quantum theory are experimentally testable relations which address the question of quantum completeness. This thesis provides feasibility results for a fermionic test of the Bell inequality, and the first known attempt to investigate the completeness question through the Wigner relation. Such a test is made possible by the production of an entangled p-p singlet at the KVI research facility in Groningen, the Netherlands, through the reactions 12C(d,2He)12B and p(d,2He)n. The p-p spin-correlations are analyzable via the KVI's 2-pi polarimeter acceptance, which eliminates loopholes common to previous experiments. The results distinguish between a hidden variables and quantum mechanical description of the universe. Also presented is a critique of the GHZ argument against the existence of local hidden variables.

Arising out of the EPR debate, the Bell and Wigner inequalities of quantum theory are experimentally testable relations which address the question of quantum completeness. This thesis provides feasibility results for a fermionic test of the Bell inequality, and the first known attempt to investigate the completeness question through the Wigner relation. Such a test is made possible by the production of an entangled p-p singlet at the KVI research facility in Groningen, the Netherlands, through the reactions 12C(d,2He)12B and p(d,2He)n. The p-p spin-correlations are analyzable via the KVI's 2-pi polarimeter acceptance, which eliminates loopholes common to previous experiments. The results distinguish between a hidden variables and quantum mechanical description of the universe. Also presented is a critique of the GHZ argument against the existence of local hidden variables.

This Master  thesis considers certain aspects of Supersymmetric Quantum Mechanics in the context of Path integral approach. First we state all the basic mathematical structure involved, and carry out some basic Gaussian integrals for both commutative and non-commutative variables. Later in the thesis these simple results obtained are generalized to study the Supersymmetric sigma models on flat and curved space. And we will recover the beautiful relationship between the supersymmetric sigma  model and the geometry of the  target manifold in the form of topological invariants of the manifold, for the models on curved space.

Thesis--Leiden. / Curriculum vitae. Includes bibliographical references.