Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'

The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell's condition of local causality.Comment: 14 pages. To be published in PSE volume "Explanation, Prediction, and Confirmation", edited by Dieks, et a

Reasons why people change their alcohol consumption in later life: findings from the Whitehall II Cohort Study.

Harmful alcohol consumption among the ageing population is an important public health issue. Very few studies ask drinkers why they change their consumption in later life. The aim of this paper was to determine whether a group of people aged over 60 years increased or decreased their alcohol consumption over the past decade and to determine the reasons for their change. We also examined whether the responses varied by age, sex and socio-economic position (SEP)

On separability of quantum states and the violation of Bell-type inequalities

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system in a separable state. We derive quantum analogues of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended CHSH inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.Comment: 13 pages, extended versio

Correlation functions, Bell's inequalities and the fundamental conservation laws

I derive the correlation function for a general theory of two-valued spin variables that satisfy the fundamental conservation law of angular momentum. The unique theory-independent correlation function is identical to the quantum mechanical correlation function. I prove that any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates the Bell's inequalities. Taken together with the Bell's theorem, this result has far reaching implications. No theory satisfying Einstein locality, reality in the EPR-Bell sense, and the validity of the conservation law can be constructed. Therefore, all local hidden variable theories are incompatible with fundamental symmetries and conservation laws. Bell's inequalities can be obeyed only by violating a conservation law. The implications for experiments on Bell's inequalities are obvious. The result provides new insight regarding entanglement, and its measures.Comment: LaTeX, 12pt, 11 pages, 2 figure

Is there contextuality for a single qubit?

It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models is not of the Kochen-Specker type. It is rather the result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between POVM elements and projectors on the extended Hilbert space and the same POVM element has to originate from two different projectors when used in Cabello's and Nakamura's models. Moreover, we propose a hidden-variable formulation of the above models.Comment: 4 pages, 1 figure, comments welcom

A simple model of quantum trajectories

Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different ``unravelings'' of a mixed state master equation. I also comment briefly on the relationship of the theory to the Consistent Histories formalism and to spontaneous collapse models.Comment: 42 pages RevTeX including four figures in encapsulated postscript. Submitted to special issue of American Journal of Physic

Maximal violation of Bell inequality for any given two-qubit pure state

In the case of bipartite two qubits systems, we derive the analytical expression of bound of Bell operator for any given pure state. Our result not only manifest some properties of Bell inequality, for example which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also give the explicit values of maximal violation for any pure state. Finally we point out that for two qubits systems there is no mixed state which can produce maximal violation of Bell inequality.Comment: 3 pages, 1 figure

Local vertical measurements and violation of Bell inequality

For two qubits belonging to Alice and Bob, we derive an approach to setup the bound of Bell operator in the condition that Alice and Bob continue to perform local vertical measurements. For pure states we find that if the entanglement of the two qubits is less than 0.2644 (measured with von Neumann entropy) the violation of the Bell inequality will never be realized, and only when the entanglement is equal to 1 the maximal violation ($2\sqrt{2}$) can occur. For specific form of mixed states, we prove that the bound of the Bell inequality depends on the concurrence. Only when the concurrence is greater than 0.6 the violation of the Bell inequality can occur, and the maximal violation can never be achieved. We suggest that the bound of the Bell operator in the condition of local vertical measurements may be used as a measure of the entanglement.Comment: 4 pages, 3 figure