Majorization and Measures of Classical Polarization in Three Dimensions

There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the polarization state space in the process. We use majorization, previously used in quantum information, as a criterion to establish a partial ordering on the polarization state space. Using this criterion and other considerations, the most useful polarization measure in three dimensions is found to be one dependent on the Bloch vector decomposition of the polarization matrix.Comment: 8 page

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fr\'echet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits. These inequalities place limits on local hidden variable models that define joint probabilities for noncommuting observables. We find Quasi-Bell inequalities have a quantum to classical violation as high as $\frac{3}{2}$, higher than conventional Bell inequalities. The result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics, and provides an insightful generalization of Bell inequalities.Comment: 17 page

POURQUOI LA THEORIE DE LA « MACROJUSTICE » MÉRITE-T-ELLE QU'ON EN DEBATTE ?

Theory of "macrojustice" [Kolm (2005)] is a stimulating contribution to the debate on the macroeconomic incomes distribution. The solution proposed by the author is the result of a three stages construction : first, agreement on the scheme of labour incomes redistribution, second, agreement on the degree of equalization to be chosen in that framework and, third, control by everyone of the intensity with which his own productive capacities (at the root of his labour income) are exploited. To begin with the core of the theory of macrojustice is defined (1.), and two specially original features are recorded (2.). Finally, five points must be questioned, because of their significance for further investigation (3)La théorie de la « macrojustice » [Kolm (2005)] est une contribution stimulante au débat contemporain sur la répartition macroéconomique des revenus. La solution préconisée ? les transferts redistributifs ELIE (« Equal Labor Income Equalization ») - résulte d'une construction à trois étages : consensus sur un schéma général de redistribution des revenus du travail, consensus sur l'intensité de l'égalisation à opérer dans ce cadre général, maîtrise par l'individu de l'intensité avec laquelle il exploite ses capacités productives personnelles, source de ces revenus. Le c?ur de la théorie de la macrojustice est d'abord présenté en ces termes (1.), puis soumis à un examen critique du double point de vue de la philosophie économique et de l'économie publique : sont recensés deux traits particulièrement originaux (2.) et cinq points controversés, mais riches de sens, pour de futurs approfondissements (3.)

Les Théories de la Justice Vues par un Économiste. De "l'Économie du Bien-Être" au "Post-Welfarisme" Contemporain

Concerning theories of justice, law and economics seem to advance along divergent lines: whereas the jurist does not argue any longer for what is "just" nor does he cares about the aim of the law, the economist again gives attention to questions of justice, which is one important subject of "economic philosophy". For a long time the debate about "old" and "new" welfare economics gave the analysis a "welfarist" orientation (I); in this paper we also glance over the main research fields explored nowadays by the economist, all of them being identified with its specific methodological approach: Rawls' "contractualism" gives access to the first "post-welfarist" field, which has renewed normative economics (II). In such a favorable context, Hayek's "evolutionism" receives more attention as a "non welfarist" theory which otherwise could have remained at the margin of the economic thought (III). Lastly, Sen's "comparatism" has become a second "post-welfarist" theory which insists on his complete autonomy towards the first one (IV). Each of these four economics-based approaches can of course be prolonged up to the domain of law