The ubiquitous theory of quantum mechanics has sparked many controversial debates about possible interpretations and its place in fundamental physical theory. Perhaps most sustained of all the questions is the quest for a complete explanation of the process behind the reduction from quantum to classical phenomena. This thesis shall examine this question through detailed investigation of specific models. The models include a careful exposition of quantum entanglement through the original EPR thought experiment for continuous variables and its mathematical transcription. The transcription is compared with existing methods from quantum optics for achieving experimentally verifiable Bell-type inequality violations, which are commonly interpreted as violations of locality. In further development of this famous paradox, the mathematical model is extended to tripartite continuous variable states, and detailed measures of their violation of locality are presented. Having carefully examined quantum phenomena by the EPR-paradox and its extension to tripartite cases, the investigation proceeds by considering the effect on quantum systems by an environment. This involves a re-examination of some well-known quantum system environment models: the spin-1/2 Spin-Boson and Kondo models, in which a two-level quantum system interacts with a bath of bosons or fermions respectively. The technicalities of the interactions are exposed in intricate detail, with a careful description of the constructive bosonisation and transformation methods involved. The thorough analysis leads to a new observation about the elliptic, or fully anisotropic, Kondo model. Importantly, the re-examination of the detailed structure of fermion-gas impurity models and their connection to quantum dissipative systems enables a comprehensive extension of the family of models to include in particular a new three-level dissipative system. To underline the importance of this model, it is shown that the model is exactly solvable by admitting a reparametrisation of the scattering matrix in terms of R-matrices which obey the Yang-Baxter equation. The examination of the interaction between the quantum and the classical concludes with an investigation of entanglement criteria in the system environment models discussed. A variational Ansatz for the ground state is used to demonstrate the numerical calculation of entropy expressions for the three-level systems, while the reynman-Hellmann Theorem is used to give inprinciple exact results for the entropy corresponding to the specific three-level model Hamiltonian introduced in this thesis. Throughout we provide several suggestions for further work, procedures for experimental verification and practical application.
The ubiquitous theory of quantum mechanics has sparked many controversial debates about possible interpretations and its place in fundamental physical theory. Perhaps most sustained of all the questions is the quest for a complete explanation of the process behind the reduction from quantum to classical phenomena. This thesis shall examine this question through detailed investigation of specific models. The models include a careful exposition of quantum entanglement through the original EPR thought experiment for continuous variables and its mathematical transcription. The transcription is compared with existing methods from quantum optics for achieving experimentally verifiable Bell-type inequality violations, which are commonly interpreted as violations of locality. In further development of this famous paradox, the mathematical model is extended to tripartite continuous variable states, and detailed measures of their violation of locality are presented. Having carefully examined quantum phenomena by the EPR-paradox and its extension to tripartite cases, the investigation proceeds by considering the effect on quantum systems by an environment. This involves a re-examination of some well-known quantum system environment models: the spin-1/2 Spin-Boson and Kondo models, in which a two-level quantum system interacts with a bath of bosons or fermions respectively. The technicalities of the interactions are exposed in intricate detail, with a careful description of the constructive bosonisation and transformation methods involved. The thorough analysis leads to a new observation about the elliptic, or fully anisotropic, Kondo model. Importantly, the re-examination of the detailed structure of fermion-gas impurity models and their connection to quantum dissipative systems enables a comprehensive extension of the family of models to include in particular a new three-level dissipative system. To underline the importance of this model, it is shown that the model is exactly solvable by admitting a reparametrisation of the scattering matrix in terms of R-matrices which obey the Yang-Baxter equation. The examination of the interaction between the quantum and the classical concludes with an investigation of entanglement criteria in the system environment models discussed. A variational Ansatz for the ground state is used to demonstrate the numerical calculation of entropy expressions for the three-level systems, while the reynman-Hellmann Theorem is used to give inprinciple exact results for the entropy corresponding to the specific three-level model Hamiltonian introduced in this thesis. Throughout we provide several suggestions for further work, procedures for experimental verification and practical application.
In recent decades there has been a resurge of interest in the foundations of quantum theory, partly motivated by new experimental techniques, partly by the emerging field of quantum information science. Old questions, asked since the seminal article by Einstein, Podolsky and Rosen (EPR), are being revisited. The work of John Bell has changed the direction of investigation by recognising that those fundamental philosophical questions can have, after all, input from experiment. Abner Shimony has aptly termed this new field of enquiry experimental metaphysics. The objective of this Thesis is to contribute to that body of research, by formalising old concepts, proposing new ones, and finding new results in well-studied areas. Without losing from sight that the appeal of experimental metaphysics comes from the adjective, every major result is followed by clear experimental proposals with detailed analysis of feasibility for quantum-atom optical setups. After setting the appropriate terminology and the basic concepts, we will start by analysing the original argument of Einstein, Podolsky and Rosen. We propose a general mathematical form for the assumptions behind the EPR argument, namely those of local causality and completeness. That formalisation entails what was termed a Local Hidden State model by Wiseman et al., which was proposed as a formalisation of the concept of steering first introduced by Schrodinger in a reply to the EPR paper. Violation of any consequences that can be derived from the assumption of that model therefore implies a demonstration of the EPR paradox. We will show how one can then re-derive the well-known EPR-Reid criterion for continuous-variables correlations, and derive new ones applicable to the spin setting considered by Bohm. The spin set-up of the EPR-Bohm was used by Bell to derive his now famous theorem demonstrating the incompatibility of the assumption of local causality and the predictions of quantum mechanics. The inequalities which bear his name can be derived for any number of discrete outcomes, but so far there has been no derivation which can be directly applied to the continuous-variables case of the original EPR paradox. We close the circle by deriving a class of inequalities which make no explicit mention about the number of outcomes of the experiments involved, and can therefore be used in continuous-variables measurements with no need for binning the continuous results into discrete ones. Apart from that intrinsic interest, these inequalities could prove important as a means to perform an unambiguous test of Bell inequalities since optical homodyne detection can be performed with high detection efficiency. The technique, which is based on a simple variance inequality, can alsobe used tore-derive alarge class of well-known Bell-type inequalities and at the same time find their quantum bound, making explicit from a formal point of view that the non-commutativity of the local operators is at the heart of the quantum violations. Finally, we address the issue of macroscopic superpositions originally sparked by the infamous cat paradox of Schrodinger. We consider macroscopic, mesoscopic and ‘S -scopic’ quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size S of a (pure-state) su-perposition, with respect to an observable X, as being the maximum difference in the outcomes of X predicted by that superposition. Such superpositions are referred to as generalised S -scopic superpositions to distinguish them from the extreme superpo-sitions that superpose only the two states that have a difference S in their prediction for the observable. We also consider generalised S -scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalised S -scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing.
Quantum information theory (QIT) is an emerging field of physics which aims to develop new methods of dealing with information by harnessing the power of quantum mechanics. Besides its potential to revolutionize the techniques of information processing and communication, it also provides novel approaches to better comprehend the foundations of quantum mechanics. Among many important problems in QIT, manipulation and dynamical characterization of correlations present in quantum systems stand out due to their relevance for the practical applications of the theory. This thesis intends to explore such correlations of quantum and classical nature from various perspectives. In particular, our discussions involve the investigation of local transformations among a class of entangled states and the examination of correlation measures in some physical models. We first examine the classification of the flip (0-1) and exchange symmetric (FES) states under local quantum operations. We study the optimal local one-shot conversions of FES states to determine the entanglement transformations that relate multiqubit FES states with the maximum possible probability of success. Next, we investigate the exchange symmetry properties of certain symmetric states when the qubits evolve according to a dephasing model which is also invariant under swap operation. We find that there exist states which do not preserve the exchange symmetry with unit probability during the time evolution, leading to the spontaneous breaking of exchange symmetry. Later, we turn our attention to the dynamics of quantum and classical correlations for qubit-qutrit systems in independent and global dephasing environments. In these cases, we demonstrate several interesting phenomena such as the transition from classical to quantum decoherence. Lastly, we investigate the thermal quantum and total correlations in the one-dimensional anisotropic XY model in transverse field. We discuss the ability of different measures to estimate the critical point of the quantum phase transition at finite temperature. We also consider the relation between correlations and the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations.
Due to their great importance, both from the fundamental and from the practical points of view, it is imperative that the various facets of the concepts of information and entanglement are explored systematically in connection with diverse physical systems and processes. These concepts are at the core of the emerging field of the Physics of Information. In this Thesis I investigate some aspects of the dynamics of information in both classical and quantum mechanical systems and then move on to explore entanglement in fermion systems by searching for novel ways to classify and quantify entanglement in fermionic systems. In Chapter 1 a brief review of the different information and entropic measures as well as of the main evolution equations of classical dynamical and quantum mechanical systems is given. The conservation of information as a fundamental principle both at the classical and quantum levels, and the implications of Landauer's theorem are discussed in brief. An alternative and more intuitive proof of the no-broadcasting theorem is also provided. Chapter 2 is a background chapter on quantum entanglement, where the differences between the concept of entanglement in systems consisting of distinguishable subsystems and the corresponding concept in systems of identical fermions are emphasized. Different measures of entanglement and relevant techniques such as majorization, are introduced. To illustrate some of the concepts reviewed here I discuss the entanglement properties of an exactly soluble many-body model which was studied in paper (E) of the publication list corresponding to the present Thesis. An alternative approach to the characterization of quantum correlations, based on perturbations under local measurements, is also briefly reviewed. The use of uncertainty relations as entanglement indicators in composite systems having distinguishable subsystems is then examined in some detail. Chapter 3 is based on papers (A) and (B) of the list of publications. Extended Landauer-like principles are developed, based amongst others on the conservation of information of divergenceless dynamical systems. Conservation of information within the framework of general probabilistic theories, which include the classical and quantum mechanical probabilities as particular instances, is explored. Furthermore, Zurek's information transfer theorem and the no-deleting theorem are generalized. Chapter 4 is based on articles (C) and (D) mentioned in the publication list, and investigates several separability criteria for fermions. Criteria for the detection of entanglement are developed based either on the violation of appropriate uncertainty relations or on inequalities involving entropic measures. Chapter 5 introduces an approach for the characterization of quantum correlations (going beyond entanglement) in fermion systems based upon the state disturbances generated by the measurement of local observables. Chapter 6 summarizes the conclusions drawn in the previous chapters. The work leading up to this Thesis has resulted in five publications in peer reviewed science research journals.
Quantum entanglement represents one of the most profound and counterintuitive phenomena in modern physics, fundamentally challenging classical notions of locality, causality, and separability. This comprehensive review examines the theoretical foundations of quantum entanglement, tracing its conceptual development from Einstein's critique of quantum mechanics through Bell's theorem to contemporary experimental verification. The paper synthesizes current understanding of entanglement's mathematical formalism, its role in violating Bell inequalities, and the resolution of the EPR paradox. Extensive discussion is devoted to landmark experiments that have conclusively demonstrated non-local correlations, including photon polarization studies, satellite-based quantum communication, and loophole-free Bell tests. The work further explores emerging technological applications in quantum cryptography, quantum computing, and quantum teleportation, while addressing fundamental questions regarding the nature of reality, information, and the relationship between quantum mechanics and general relativity. Finally, the paper examines open questions and speculative frameworks suggesting that entanglement may represent a foundational principle underlying spacetime geometry itself. Video documentation of this analysis is available at: https://www.youtube.com/watch?v=YDGKuXYRPpI.
Quantum entanglement stands as one of the most profound and non-intuitive phenomena in quantum mechanics, challenging classical notions of locality and realism. This study explores the foundational principles, experimental validations, and technological implications of quantum entanglement within the broader context of the quantum world. Drawing from both historical milestones and recent advancements, the research investigates how entangled states emerge, evolve, and influence the behavior of spatially separated quantum systems. Using a mixed-methods approach that integrates theoretical analysis with quantitative simulation, this paper demonstrates how entanglement defies classical correlations by revealing statistical patterns that violate Bell-type inequalities. Results from simulated EPR-Bohm-type experiments show consistent alignment with quantum mechanical predictions, reinforcing the non-local character of entangled systems. Furthermore, we assess how entanglement underpins emerging technologies such as quantum computing, quantum teleportation, and secure quantum communication. Visual representations—including density matrices, correlation plots, and entanglement entropy graphs—are employed to interpret the complexity of multipartite systems and decoherence dynamics. The findings not only affirm the robustness of quantum entanglement as a theoretical construct but also highlight its real-world applications and philosophical implications. Ultimately, this study confirms that understanding quantum entanglement is not merely a conceptual pursuit but a crucial step toward harnessing the quantum world for next-generation technologies and deeper inquiries into the fabric of reality.
We study the relationship between one-dimensional fermion gas-impurity models and quantum dissipative systems, via the method of constructive bosonisation and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer model, a new, exactly solvable, three-level quantum dissipative system is derived as a generalisation of the standard spin-half spin-boson model. The new system has two environmental oscillator baths with ohmic coupling, and admits arbitrary detuning between the three levels. All tunnelling matrix elements are equal, up to one complex phase which is itself a function of the longitudinal and transverse couplings in the integrable limit. Our work underlines the importance of re-examining the detailed structure of fermion-gas impurity models and spin chains, in the light of connections to models for quantum dissipative systems.