We draw systematic parallels between the measurement problem in quantum mechanics and the information loss problem in black holes. Then we proceed to propose a solution of the former along the lines of the solution of the latter which is based on the holographic gauge/gravity duality. The proposed solution is based on 1) the quantum dualism between the local view of reality provided by Copenhagen and the manifold view provided by the many-worlds and on 2) the properties of quantum entanglement in particular its fungibility.
We draw systematic parallels between the measurement problem in quantum mechanics and the information loss problem in black holes. Then we proceed to propose a solution of the former along the lines of the solution of the latter which is based on the holographic gauge/gravity duality. The proposed solution is based on 1) the quantum dualism between the local view of reality provided by Copenhagen and the manifold view provided by the many-worlds and on 2) the properties of quantum entanglement in particular its fungibility.
For over a century, scientists have been fascinated by the strange behaviour of matter at the quantum level, where particles can exist in many states at once and affect each other instantly across distances. This paper explores this realm of quantum mechanics by focusing on wave–particle duality, superposition, entanglement and the measurement problem. It shows how these concepts defy the foundations of clas-sical physics to challenge assumptions about determinism, locality, interconnection and objectivity. The paper maintains that although quantum theory works remarkably well, we lack a clear account of what kind of reality it describes, as major interpretations such as Copenhagen, Many-Worlds and objective collapse still struggle to match quantum theory’s success with a clear picture of reality. yet as its major interpretations offer com-peting and unresolved pictures of the world. Schrödinger’s cat illustrates this tension to showcase how macroscopic systems can expose the limits of observation and the line be-tween classical and quantum worlds. The paper concludes that these quantum principles are underpinned by both technical and philosophical challenges and they force us to re-think causality and the role of the observer in explaining reality.
This thesis consists of four research papers and an introduction covering the most important concepts appearing in the papers. The papers deal with applications of gauge/gravity dualities in the study of various physical quantities and systems. Gauge/gravity dualities are equivalences between certain quantum field theories and classical theories of gravity. These dualities can be used as computational tools in a wide range of applications across different fields of physics, and as such they have garnered much attention in the last two decades. The great promise of these new tools is the ability to tackle difficult problems in strongly interacting quantum field theories by translating them to problems in classical gravity, where progress is much easier to make. Quantum information theory studies the information contained in quantum systems. Entanglement is the fundamental property of quantum mechanics that sets it apart from classical theories of physics. Entanglement is commonly quantified by entanglement entropy, a quantity which is difficult to compute in interacting quantum field theories. Gauge/gravity dualities provide a practical way for computing the entanglement entropy via the Ryu-Takayanagi formula. The primary focus of this thesis is to use this formula for computing various entanglement measures in strongly interacting quantum field theories via their gravity duals. The purpose of this thesis is to introduce quantum information theory concepts that have been important in our research. When applicable, quantities of interest are first introduced in the classical setting in order to build intuition about their behaviour. Quantum properties of entanglement measures are discussed in detail, along with their holographic counterparts, and remarks are made concerning their applications.
This work presents a historical-epistemological analysis of the foundations of quantum mechanics. From a philosophical point of view, the relationships between quantum mechanics and scientific realism are highlighted, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of measurement in the context of quantum mechanics is underlined, as an essential element in providing a coherent description of reality moving from the microcosm to the macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the ontological problem, the problem of the objectification of the wave function and the problem of the definition of discernibility. This is followed by an overview of the most important alternative proposals to the standard interpretation (Copenhagen interpretation), with particular reference to hidden variable theories, and other alternatives to standard quantum mechanics that profoundly modify the vision of reality, such as the Everett’s many-worlds theory, the QBism, the unified holistic approach.
We give a pedagogical review of how concepts from quantum information theory build up the gravitational side of the anti-de Sitter/conformal field theory correspondence. The review is self-contained in that it only presupposes knowledge of quantum mechanics and general relativity; other tools-including holographic duality itself-are introduced in the text. We have aimed to give researchers interested in entering this field a working knowledge sufficient for initiating original projects. The review begins with the laws of black hole thermodynamics, which form the basis of this subject, then introduces the Ryu-Takayanagi proposal, the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) relation, and subregion duality. We discuss tensor networks as a visualization tool and analyze various network architectures in detail. Next, several modern concepts and techniques are discussed: Rényi entropies and the replica trick, differential entropy and kinematic space, modular Berry phases, modular minimal entropy, entanglement wedge cross-sections, bit threads, and others. We discuss the extent to which bulk geometries are fixed by boundary entanglement entropies, and analyze the relations such as the monogamy of mutual information, which boundary entanglement entropies must obey if a state has a semiclassical bulk dual. We close with a discussion of black holes, including holographic complexity, firewalls and the black hole information paradox, islands, and replica wormholes.
The work presented in this thesis is a contribution towards the understanding of holo- graphic entanglement from an operational perspective. Following the interpretation which is most natural for quantum information theory, entanglement is viewed as a resource that can be produced, stored, transferred and used for practical purposes. The first chapter introduces the main concepts which are necessary throughout the discussion. Quantum entanglement, as opposed to merely classical correlation, is presented in detail within the framework of quantum mechanics. This is followed by a brief overview on the current state of knowledge about entanglement in quantum field theory and more specifically in gauge/gravity duality. The second chapter investigates a particular measure of entanglement, known as nega- tivity, in the context of holographic field theories. This is further explored in the following (third) chapter, where an interesting dependence of the entanglement between a region and its complement on the topology of their interface is presented. The forth chapter investigates qubits systems and compares equivalence classes of entanglement structures to known properties of holographic states. The fifth chapter focuses on the behaviour of the tripartite information for highly en- tangled states, both in a bipartite and multipartite sense, in relation to the sign definiteness imposed by holography. A final chapter comments on future directions of investigation within this program.