One of the most important problems in physics is to reconcile quantum mechanics with general relativity, and some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favour of a more general theory. Here, we propose a mechanism to make general claims on the microscopic structure of the Universe by postulating that any post-quantum theory should recover classical physics in the macroscopic limit. We use this mechanism to bound the strength of correlations between distant observers in any physical theory. Although several quantum limits are recovered, such as the set of two-point quantum correlators, our results suggest that there exist plausible microscopic theories of Nature that predict correlations impossible to reproduce in any quantum mechanical system.
One of the most important problems in physics is to reconcile quantum mechanics with general relativity, and some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favour of a more general theory. Here, we propose a mechanism to make general claims on the microscopic structure of the Universe by postulating that any post-quantum theory should recover classical physics in the macroscopic limit. We use this mechanism to bound the strength of correlations between distant observers in any physical theory. Although several quantum limits are recovered, such as the set of two-point quantum correlators, our results suggest that there exist plausible microscopic theories of Nature that predict correlations impossible to reproduce in any quantum mechanical system.
One of the main unsolved question in Quantum Mechanics (QM) is its compatibility with classical mechanics. The laws of QM, which describe the microscopic world, must merge into the classical ones for large enough physical systems, but it is still unknown at which point, if any, the transition occurs and if the transition is smooth or sudden as the size increases. Furthermore, a strict extension of QM to the macroscopic world leads to well known 'paradoxes', which is not straightforward to solve. This question is tightly connected with the measurement problem, since any measurement apparatus must give a response which can be described at classical level. Many experiments have been performed to answer to this question. They mainly try to find to which extent the number of particles can be increased in order to observe clear evidence of violation of standard QM. In this paper we argue that the macroscopicity parameter is not the number of particles but the number of independent degrees of freedom, as proposed in a recent model for the completion of QM. This introduces a sort of change of paradigm. To support this claim a representative set of well known experiments are analyzed from this point of view. This brings to a new interpretation of the experiments. A general scheme for the quantum-classical transition is discussed in some details.
Quantum mechanics has achieved unparalleled success as an operational theory, describing a wide range of experiments to remarkable accuracy. However, the physical foundations on which it rests remain as puzzling as they were a century ago, and a concise statement of the physical principles that underlie quantum mechanics is still outstanding. One promising approach holds that these principles should be formulated in terms of information, since many of the counter-intuitive effects in quantum theory concern questions such as what one can know about a quantum system and how the information encoded therein can be processed and distributed between parties. Another challenging feature of quantum theory is its incompatibility with the other cornerstone of modern physics, general relativity. In order to reconcile the two, one must identify and retain only the essential concepts and principles of each theory, and in the case of general relativity, causality has been identified as such a concept. This raises the question of how our classical understanding of causality must change when quantum theory is taken into account. In order to address these questions about information, knowledge and causality, I turn to the framework of causal models. In classical statistics, causal models explain the relations among a set of variables in terms of causal influences, which makes them a powerful tool for structuring our knowledge about complex systems and developing strategies for interacting with them. More importantly, the framework provides the conceptual underpinnings and mathematical methods for addressing questions about causation, information and knowledge in a rigorous manner. In this thesis, I develop a version of the classical causal models framework that is compatible with quantum theory and explore its physical implications. \n \n \nA first step is to define quantum versions of fundamental elements such as variables, conditionals and belief propagation rules. This allows one to consider the question of what one can come to know about a quantum variable from the point of view of causal modelling. The conditionals relating quantum variables are found to have a richer structure than their classical counterparts, which can be exploited for the task of discerning causal relations given limited data -- a central problem in classical causal modelling. The mathematical properties of quantum conditionals also establish a correspondence between various classes of two-party correlations, such as bound and distillable entanglement, and the types of causal structures that can give rise to them, which may become a useful tool for entanglement theory and quantum information processing. In the context of open quantum systems dynamics, quantum causal models provide a clear physical explanation of not completely positive maps and, more broadly, of non-Markovian quantum dynamics. Finally, I consider the possibility of non-classical effects in the way that different causal mechanisms are combined -- that is, non-classical causal structures. For the simple case of two causally ordered variables, I propose indicators that witness different classes of combinations of causal mechanisms, including a non-classical mixture, and describe an experiment realizing examples of the different classes. \n \n \nAs these results illustrate, the framework of quantum causal models provides both greater conceptual clarity and a comprehensive mathematical formalism for studying a diverse set of problems, ranging from foundational questions to applications in open systems dynamics and the exploration of non-classical causal structures, which are likely to feature in a future theory of quantum gravity. The material presented in this thesis is intended as a foundation and inspiration for further applications of quantum causal models.
Conceptually different from the decoherence program, we present a novel theoretical approach to macroscopic realism and classical physics within quantum theory. It focuses on the limits of observability of quantum effects of macroscopic objects, i.e., on the required precision of our measurement apparatuses such that quantum phenomena can still be observed. First, we demonstrate that for unrestricted measurement accuracy, no classical description is possible for arbitrarily large systems. Then we show for a certain time evolution that under coarse-grained measurements, not only macrorealism but even classical Newtonian laws emerge out of the Schrödinger equation and the projection postulate.
In this thesis we present methods to efficiently verify quantum many-body experiments. The first part focuses on the quantitative verification of graph state experiments from simple measurements. In particular, optimal bounds on the fidelity, purity and entropy from stabilizer measurements are derived as well as high-quality bounds on entanglement measures. Furthermore, we show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory, and a lower bound to the entanglement can be read off directly from the scattering cross section of neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. Quantum mechanics offers many interesting properties such as entanglement and non-locality. However, one can easily think of more general correlations than quantum correlations. This gives rise to the question if quantum correlations are the most general allowed in nature? In the last part we propose a new axiom we call macroscopic locality. The idea behind this axiom is that any physical theory should recover classical physics in the continuum limit (i.e., when a large number of particles is involved and our measurement devices fail to resolve discrete particles). We will show that this very intuitive axiom, together with the no-signaling principle, allows to recover many important results in quantum mechanics, like the universality of the Tsirelson bound, or the set of accessible two-point correlators. Moreover, we will provide a complete characterization of the correlations between two distant physical systems that arise out of both axioms and comment on its consistency.
The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from quantum mechanics in the macroscopic limit. In this paper, we challenge this perspective and demonstrate that the behaviour of a macroscopic system can retain all aspects of the quantum formalism, in a way that is robust against decoherence, particle losses and coarse-grained (imprecise) measurements. This departure from the expected classical description of macroscopic systems is not merely mathematical but also conceptual, as we show by the explicit violation of a Bell inequality and a Leggett–Garg inequality.
Identity principle is a fundamental postulate of quantum mechanics. In this paper, from a philosophical point of view, we revisit the identity principle of quantum mechanics. We attribute the identity to the existence of a precision limit for observation: the microscopic objects become indistinguishable when the difference between them is lower than the precision limit. This precision limit is determined not by the measuring apparatus, but by the action quantum h behand the objective physical law. We deduce logically how to relate the identity principle with the probabilistic interpretation, uncertainty principle, quantization in quantum mechanics, attempting to sorting out some logic for quantum theory. The indistinguishability of identical particles makes it impossible to accurately obtain all the details about the microscopic objects at the same time, and consequently the microscopic objects can only be described statistically, leading to the probabilistic determinism and indeterminacy of initial state in quantum mechanics. By reviewing Bohmian mechanics, one of the nonlocal hidden variable theories, we discuss the possibility of restoring determinism and causality in quantum mechanics by restoring the determinacy of initial state. However, any hidden variable theory constructed by using only the terminologies of classical physics cannot reproduce the quantum mechanical predictions. It is the identity principle that makes it impossible to restore causality and determinism, and is the root that makes quantum mechanics different from classical physics. Finally, the boundary between the so-called classical and quantum worlds is discussed. We hope these philosophical arguments can provide a kind of epistemic understanding for quantum mechanics.