Parts and Wholes. An Inquiry into Quantum and Classical Correlations

Abstract

** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. ** A large part of this dissertation is devoted to understanding different aspects of four different kinds of correlations: local, partially-local, no-signaling and quantum mechanical correlations. Novel characteristics of these correlations have been used to study how they are related and how they can be discerned via Bell-type inequalities that give non-trivial bounds on the strength of the correlations. ** The study of quantum correlations has also prompted us to study a) the multi-partite qubit state space with respect to its entanglement and separability characteristics, and b) the differing strength of the correlations in separable and entangled qubit states. Results include a novel classification of multipartite (partial) separability and entanglement, strong constraints on the monogamy of entanglement and of non-local correlations, and many new entanglement detection criteria that are directly experimentally accessible. ** Because of the generality of the investigation these results also have strong foundational as well as philosophical repercussions for the different sorts of physical theories as a whole; notably for the viability of hidden variable theories for quantum mechanics, for the possibility of doing experimental metaphysics, for the question of holism in physical theories, and for the classical vs. quantum dichotomy.

Dissertation, Utrecht University, 2008. 286 pages. ISBN: 978-90-3934916-8. A hard copy is obtainable via Igitur of the Utrecht University Library. This version 3 has exactly the same content as the version 2. Only the page layout has been changed to match the hard copy layout of the Dissertation which is on B5 format

References in corpus (39)

• Three qubits can be entangled in two inequivalent ways
• Scalable multi-particle entanglement of trapped ions
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Quantum Nonlocality without Entanglement
• Observation of three-photon Greenberger-Horne-Zeilinger entanglement
• Bell Inequalities and the Separability Criterion
• Unextendible Product Bases and Bound Entanglement
• Alice falls into a black hole: Entanglement in non-inertial frames
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• Witnessing multipartite entanglement
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• Detection of entanglement with few local measurements
• Bell inequality, Bell states and maximally entangled states for n qubits
• Multipartite entanglement in spin chains
• Quantum Communication between N partners and Bell's inequalities
• Geometry of entangled states
• Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations
• A four-party unlockable bound-entangled state
• Toolbox for entanglement detection and fidelity estimation
• Experimental detection of entanglement via witness operators and local measurements
• Interconversion of Nonlocal Correlations
• Sufficient conditions for three-particle entanglement and their tests in recent experiments
• Partial separability and entanglement criteria for multiqubit quantum states
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• On experimental procedures for entanglement verification
• Investigating three qubit entanglement with local measurements
• The Extent of Multi-particle Quantum Non-locality
• Multiparticle entanglement and its experimental detection
• Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
• No time loophole in Bell's theorem; the Hess-Philipp model is non-local
• Two-Setting Bell Inequalities for Many Qubits
• Entanglement and Relativity
• Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"
• Multiqubit entanglement witness
• The quantum world is not built up from correlations
• Strengthened Bell inequalities for orthogonal spin directions
• Inequalities that test locality in quantum mechanics
• Bell Inequalities Classifying Bi-separable Three-qubit States

Cited by in corpus (10)

• Entanglement detection
• Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side
• Entangled quantum states in a local deterministic theory
• The Cellular Automaton Interpretation of Quantum Mechanics
• Constraints on determinism: Bell versus Conway-Kochen
• How a wave function can collapse without violating Schroedinger's equation, and how to understand Born's rule
• Quantum Mechanics: From Realism to Intuitionism
• A Flea on Schroedinger's Cat
• A Stronger Bell Argument for (Some Kind of) Parameter Dependence
• The basic Leggett inequalities don't contradict the quantum theory, neither the classical physics