Quantum nonlocality test for continuous-variable states with dichotomic observables

There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and the presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous-variable state. However, it does not have to be a maximally entangled state to give the maximal violation of Bell's inequality. This is attributed to a generic problem of testing the quantum nonlocality of an infinite- dimensional state using a dichotomic observable.

d-outcome measurement for a nonlocality test

For the purpose of a nonlocality test, we propose a general correlation observable of two parties by utilizing local d- outcome measurements with SU(d) transformations and classical communications. Generic symmetries of the SU(d) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser- Home-Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, leads to the Collins-Gisin-Linden-Massar-Popescu (CGLMP) nonlocality test for d-outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous- variable (CV) entangled state with d measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for d(greater than or equal to2) measurement outcomes when the observables are of SU(d) transformations.

Joint measurements and Bell inequalities

Joint quantum measurements of noncommuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

Quantum nonlocality for a mixed entangled coherent state

Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality, the more rapidly quantum nonlocality is lost. The entangled coherent state can also be investigated in the framework of 2x2 Hilbert space. The quantum nonlocality persists longer in 2x2 Hilbert space. When it decoheres it is found that the entangled coherent state fails the nonlocality test, which contrasts with the fact that the decohered entangled state is always entangled.

Integrating Ballymun? Flawed progress in Ireland's largest estate regeneration scheme

Urban regeneration in the Republic of Ireland takes place in the context of the rapid, ‘Celtic Tiger’ economic growth of the 1990s. The boom transformed Irish society and led to greater affluence for many people, along with continuing and arguably worsening inequality for those excluded from its opportunities. In particular, Ireland’s small social rented sector has become the focus of the country’s most concentrated poverty and social exclusion. The Ballymun regeneration programme in North Dublin aims to facilitate physical, social and economic change in order to integrate the area more closely with the
more affluent surrounding suburbs. This article reviews the issues involved in restructuring such a large area of social exclusion within a rapidly changing European capital city, using a framework that disaggregates the concept of integration into three elements: market, citizenship and reciprocity. With just over half the physical refurbishment complete, progress has been made but some fundamental issues remain. The article concludes that although substantial advancement has been made with physical regeneration, progress with wider economic and social integration has been uneven and in some cases flawed.

Failure of Local Realism Revealed by Extremely-Coarse-Grained Measurements

We show that failure of local realism can be revealed to observers for whom only extremely-coarse-grained measurements are available. In our instances, Bell's inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. Furthermore, we can observe failure of local realism when an inequality enforced by nonlocal realistic theories is satisfied. This suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. Small-scale experimental demonstration of our examples may be possible in the foreseeable future.

Unconditional constants and polynomial inequalities

If P is a polynomial on Rm of degree at most n then we define the polynomial |P|. Now if B is a convex compact set in Rm, we define the norm ||P||B of P as the maximum of P on B, and then we investigate the inequality || |P| ||B

Social psychology and peace: An introductory overview

This paper begins by giving an overview of why and in which ways social psychological research can be relevant to peace. Galtung's (1969) distinction between negative peace (the absence of direct violence) and positive peace (the absence of structural violence, or the presence of social justice) is crossed with a focus on factors that are detrimental (obstacles) to peace versus factors that are conducive to peace (catalysts), yielding a two-by-two classification of social psychological contributions to peace, Research falling into these four classes is cited in brief, with a particular focus on four exemplary topics: support for military interventions as an obstacle to negative peace; antiwar activism as a catalyst of negative peace; ideologies legitimizing social inequality as an obstacle to positive peace; and commitment to human rights as a catalyst of positive peace. Based on this conceptual framework, the remaining six articles of the special issue

Multiple osteochondromas in the archaeological record: a global review

Multiple osteochondromas is an inherited autosomal dominant condition of enchondral bone growth. The paper undertakes the first synthesis study of the 16 known cases of the condition that have been identified in the international palaeopathological record. It also includes information derived from two newly discovered cases of the disease in two adult male individuals recovered from the Medieval cemetery at Ballyhanna, Co. Donegal, Ireland. The formation of multiple osteochondromas is the best known characteristic of the disease but it also involves the development of a suite of orthopaedic deformities. These deformities, which include disproportionate short stature, inequality of bone length, forearm deformities, tibiofibular diastasis, coxa valga of the hip and valgus deformity of the knee and ankle, are discussed in relation to the archaeological cases. Numerous synonyms for the disease have been used within the various publications produced by palaeopathologists, and this can generate confusion among readers. As such, the paper recommends that in future palaeopathologists should follow the guidance of the World Health Organization and use the term multiple osteochondromas when discussing the disease.

Wealth concentration in the European periphery: Ireland, 1858–2001

Using annual will indexes, a series of wealth concentration is constructed for the north of Ireland on a decennial basis for the period 1858 to 2001. Wealth was highly concentrated at the beginning of the sample period, but inequality falls towards the end of the nineteenth century and continues to fall until the 1970s. However, there does not appear to be a Kuznets-type process at work. Instead, using data on socio-occupational status, it is suggested that the fall in wealth concentration appears to be associated with the demise of the titled classes. Interestingly, similar to the findings of other studies, wealth has become more concentrated since the 1970s.

‘It ain’t easy being green’: Sustainable Development between Environment and Economy in Northern Ireland’

Given the relative lack of research on sustainable development in Northern Ireland, this paper focuses on the tensions between environmental governance and regulation on the one hand, and the ‘post-conflict’ imperative for Northern Ireland to compete and grow as a regional economy without continued British state subvention and subsidisation. The paper outlines how this ‘trade-off’ between ‘environment’ and ‘economy’ is essentially misplaced. It argues that this trade-off can be avoided if there is a shift in focus from an ‘environment versus the economy’ policy position to one in which the ‘triple bottom line’ (social, economic and environmental) of sustainable development becomes the over-arching policy agenda. Sustainable development, unlike either orthodox environmental or economic policy, also connects centrally with the unique ‘post-conflict transformation’ agenda of Northern Ireland. For example, promoting a human rights civic culture, tackling socioeconomic inequality and social exclusion, and building a shared future based on supporting sustainable communities and an innovative model of a ‘green(ing) economy’ goes beyond orthodox economic growth. However, it is clear from the Executive’s Programme for Government, failure to support the creation of an independent Environment Protection Agency, and above all the prioritisation of orthodox economic growth based on foreign direct investment that neither environmental protection nor sustainable development is or will be high on the political or policy agenda in Northern Ireland.

Paradoxes unbounded: Practising community making

The first section of this paper is a discussion of the paradoxes contained in the word ‘community’, which deliberately foregrounds and problematises these conflicting meanings before arguing for a third definition and practice of community that transcends and even celebrates contradictions within an active learning model of education in the community aimed at tackling inequality and prejudice. The second section offers an autocritical narrative account of an education in the community project which illustrates how such a practice of community making can be achieved within an educational framework in which pupil is teacher and teacher is pupil. The paper draws upon theoretical models from the fields of community development, inclusive and creative education, emancipatory action research, postmodernism and postcolonialism.

Testing quantum contextuality of continuous-variable states

We investigate the violation of noncontextuality by a class of continuous-variable states, including variations of entangled coherent states and a two-mode continuous superposition of coherent states. We generalize the Kochen-Specker (KS) inequality discussed by Cabello [A. Cabello, Phys. Rev. Lett. 101, 210401 (2008)] by using effective bidimensional observables implemented through physical operations acting on continuous-variable states, in a way similar to an approach to the falsification of Bell-Clauser-Horne-Shimony-Holt inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudospin observables and a generalized quasiprobability function.

Non-locality of two ultracold trapped atoms

We undertake a detailed analysis of the non-local properties of the fundamental problem of two trapped, distinguishable neutral atoms that interact with a short-range potential characterized by an s-wave scattering length. We show that this interaction generates continuous variable (CV) entanglement between the external degrees of freedom of the atoms and consider its behaviour as a function of both, the distance between the traps and the magnitude of the inter-particle scattering length. We first quantify the entanglement in the ground state of the system at zero temperature and then, adopting a phase-space approach, test the violation of the Clauser-Horn-Shimony-Holt inequality at zero and non-zero temperature and under the effects of general dissipative local environments.

Faithful test of nonlocal realism with entangled coherent states

We investigate the violation of Leggett's inequality for nonlocal realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the nonlocal realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows one to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original arguments to continuous-variable states.