No-signaling, perfect bipartite dichotomic correlations and local randomness

The no-signaling constraint on bi-partite correlations is reviewed. It is shown that in order to obtain non-trivial Bell-type inequalities that discern no-signaling correlations from more general ones, one must go beyond considering expectation values of products of observables only. A new set of nontrivial no-signaling inequalities is derived which have a remarkably close resemblance to the CHSH inequality, yet are fundamentally different. A set of inequalities by Roy and Singh and Avis et al., which is claimed to be useful for discerning no-signaling correlations, is shown to be trivially satisfied by any correlation whatsoever. Finally, using the set of newly derived no-signaling inequalities a result with potential cryptographic consequences is proven: if different parties use identical devices, then, once they have perfect correlations at spacelike separation between dichotomic observables, they know that because of no-signaling the local marginals cannot but be completely random.Comment: Published in 'Proceedings of the International Conference Advances in Quantum Theory', AIP Conference Proceedings, vol. 1327, 2011. pp. 36-5

Can quantum theory and special relativity peacefully coexist?

This white paper aims to identify an open problem in 'Quantum Physics and the Nature of Reality' --namely whether quantum theory and special relativity are formally compatible--, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.Comment: Invited white paper for Quantum Physics and the Nature of Reality, John Polkinghorne 80th Birthday Conference. St Anne's College, Oxford. 26-29 September 201

Strengthened Bell inequalities for orthogonal spin directions

We strengthen the bound on the correlations of two spin-1/2 particles (qubits) in separable (non-entangled) states for locally orthogonal spin directions by much tighter bounds than the well-known Bell inequality. This provides a sharper criterion for the experimental distinction between entangled and separable states, and even one which is a necessary and sufficient condition for separability. However, these improved bounds do not apply to local hidden-variable theories, and hence they provide a criterion to test the correlations allowed by local hidden-variable theories against those allowed by separable quantum states. Furthermore, these bounds are stronger than some recent alternative experimentally accessible entanglement criteria. We also address the issue of finding a finite subset of these inequalities that would already form a necessary and sufficient condition for non-entanglement. For mixed state we have not been able to resolve this, but for pure states a set of six inequalities using only three sets of orthogonal observables is shown to be already necessary and sufficient for separability.Comment: v2: Considerably changed, many new and stronger results v3: Published version; To appear in Physics Letters A. Online available from publishers websit

Discerning Elementary Particles

We extend the quantum-mechanical results of Muller & Saunders (2008) establishing the weak discernibility of an arbitrary number of similar fermions in finite-dimensional Hilbert-spaces in two ways: (a) from fermions to bosons for all finite-dimensional Hilbert-spaces; and (b) from finite-dimensional to infinite-dimensional Hilbert-spaces for all elementary particles. In both cases this is performed using operators whose physical significance is beyond doubt.This confutes the currently dominant view that (A) the quantum-mechanical description of similar particles conflicts with Leibniz's Principle of the Identity of Indiscernibles (PII); and that (B) the only way to save PII is by adopting some pre-Kantian metaphysical notion such as Scotusian haecceittas or Adamsian primitive thisness. We take sides with Muller & Saunders (2008) against this currently dominant view, which has been expounded and defended by, among others, Schr\"odinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Mittelstaedt, Giuntini, Castellani, Krause and Huggett.Comment: Final Version. To appear in Philosophy of Science, July 200

The quantum world is not built up from correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of J.S. Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.Comment: Published version. Title change

Parts and Wholes. An Inquiry into Quantum and Classical Correlations

** 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.Comment: 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 forma

Three-particle entanglement versus three-particle nonlocality

The notions of three-particle entanglement and three-particle nonlocality are discussed in the light of Svetlichny's inequality [Phys. Rev. D 35, 3066 (1987)]. It is shown that there exist sets of measurements which can be used to prove three-particle entanglement, but which are nevertheless useless at proving three-particle nonlocality. In particular, it is shown that the quantum predictions giving a maximal violation of Mermin's three-particle Bell inequality [Phys. Rev. Lett. 65, 1838 (1990)] can be reproduced by a hybrid hidden variables model in which nonlocal correlations are present only between two of the particles. It should be possible, however, to test the existence of both three-particle entanglement and three-particle nonlocality for any given quantum state via Svetlichny's inequality.Comment: REVTeX4, 4 pages, journal versio