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

Rare or threatened vascular plant species of Wollemi National Park, central eastern New South Wales

Wollemi National Park (c. 32o 20’– 33o 30’S, 150o– 151oE), approximately 100 km north-west of Sydney, conserves over 500 000 ha of the Triassic sandstone environments of the Central Coast and Tablelands of New South Wales, and occupies approximately 25% of the Sydney Basin biogeographical region. 94 taxa of conservation significance have been recorded and Wollemi is recognised as an important reservoir of rare and uncommon plant taxa, conserving more than 20% of all listed threatened species for the Central Coast, Central Tablelands and Central Western Slopes botanical divisions. For a land area occupying only 0.05% of these divisions, Wollemi is of paramount importance in regional conservation. Surveys within Wollemi National Park over the last decade have recorded several new populations of significant vascular plant species, including some sizeable range extensions. This paper summarises the current status of all rare or threatened taxa, describes habitat and associated species for many of these and proposes IUCN (2001) codes for all, as well as suggesting revisions to current conservation risk codes for some species. For Wollemi National Park 37 species are currently listed as Endangered (15 species) or Vulnerable (22 species) under the New South Wales Threatened Species Conservation Act 1995. An additional 50 species are currently listed as nationally rare under the Briggs and Leigh (1996) classification, or have been suggested as such by various workers. Seven species are awaiting further taxonomic investigation, including Eucalyptus sp. ‘Howes Swamp Creek’ (Doherty 26), known from a single location within the park, and Pultenaea sp. (Olinda) from Dunns Swamp – both these species remain undescribed, but are listed as endangered species. After applying IUCN criteria to the 94 taxa, 2 are considered Critically Endangered; 11 are considered Endangered; 23 are considered Vulnerable; 3 are considered Near Threatened; 19 are considered Data Deficient; and 36 are considered of Least Concern. It is likely that additional highly restricted plant taxa await discovery in remote locations

Maximal abelian and Curci-Ferrari gauges in momentum subtraction at three loops

The vertex structure of QCD fixed in the maximal abelian gauge (MAG) and Curci-Ferrari gauge is analysed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently the three loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.Comment: 23 latex pages, 4 figures, anc directory contains txt files with electronic version of renormalization group functions, coupling constant mappings, conversion functions and amplitudes in analytic form for each gaug

Bilinear quark operator renormalization at generalized symmetric point

We compute Green's functions with a bilinear quark operator inserted at non-zero momentum for a generalized momentum configuration to two loops. These are required to assist lattice gauge theory measurements of the same quantity in matching to the high energy behaviour. The flavour non-singlet operators considered are the scalar, vector and tensor currents as well as the second moment of the twist-2 Wilson operator used in deep inelastic scattering for the measurement of nucleon structure functions.Comment: 19 latex pages, 4 figures, anc directory contains electronic version of amplitude

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

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

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

The local content of all pure two-qubit states

The (non-)local content in the sense of Elitzur, Popescu, and Rohrlich (EPR2) [Phys. Lett. A 162, 25 (1992)] is a natural measure for the (non-)locality of quantum states. Its computation is in general difficult, even in low dimensions, and is one of the few open questions about pure two-qubit states. We present a complete solution to this long-lasting problem.Comment: 9 pages, 3 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