Coherent states and the reconstruction of pure spin states

Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s + 1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeros of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stem-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase space which are smaller than (h) over bar

Revisiting Mead on Pragmatic "Fusion": From Emotion to Function

A recent biography and re-issue of George H. Mead's Mind, Self, and Society emphasize the emergent meanings of his work and of self's cognitive and affective dimensions in interaction. Erving Goffman likewise posits an interaction order based on individual and social identity. Mead's metaphor of fusion furthers recognition of an emotional merging of selves with each other and with emerging community. He initially characterizes this experience as "precious" and illustrates its presence in interactional domains such as teamwork, religion, and patriotism. Among other scholars, Charles Taylor uses fusion to interpret aspects of the contemporary secular age. Application to terrorist identities finds that emotional fusion motivates actions that threaten the moral imperative informing presentation of selves that grounds public order. From a pragmatic perspective, selves in pluralistic contexts must subordinate emotional fusion to functional fusion within an interaction order that fosters a larger self and more inclusive community to address common issues

Multivariate Copula Models at Work: Outperforming the desert island copula?

Since the pioneering work of Embrechts and co-authors in 1999, copula models enjoy steadily increasing popularity in finance. Whereas copulas are well-studied in the bivariate case, the higher-dimensional case still offers several open issues and it is by far not clear how to construct copulas which sufficiently capture the characteristics of financial returns. For this reason, elliptical copulas (i.e. Gaussian and Student-t copula) still dominate both empirical and practical applications. On the other hand, several attractive construction schemes appeared in the recent literature prom sing flexible but still manageable dependence models. The aim of this work is to empirically investigate whether these models are really capable to outperform its benchmark, i.e. the Student-t copula (which is termed by Paul Embrechts as "desert island copula" on account of its excellent fit to financial returns) and, in addition, to compare the fit of these different copula classes among themselves. --KS-copula,Hierarchical Archimedian,Product copulas,Pair-copula decomposition

Interfacing Catholic Social Meanings, Sociology, Self, and Pedagogical Practices

What connects Catholic Social Tradition with Sociology? How do each inform the other and how do they, together, flow through and animate the sociologist? Within a student-driven learning community pedagogy, this course builds on the humanistic aspects of Sociology as a scientific perspective a la Peter Berger’s Invitation to Sociology. This foundation is then filtered through a social psychological understanding of self with a sense of vocation through which persons’ deepest passions meets humans’ greatest needs. Biographical vignettes of sociologists’ careers of study that address issues of racial and gender inequalities and psycho-social shifts in values over the life course exemplify linkage of social science and social justice. These portrayals of scientist-activists’ dedication to describing and explaining inequalities are complimented by case studies of sociologically-informed community activists struggling to change unjust structures and empower disadvantaged communities through initiatives that embody efforts to “live the Catholic Social Tradition.” Themes of humanistic social science, self and vocation, committed social scientists, and empowering community organizers for a more just society are then woven into an overview of Catholic Social Tradition around issues of globalization, spirituality, and justice. Finally, the course moves toward the universal issues developed within the larger Catholic social tradition—namely, common good, universal solidarity, personal dignity, and institutional subsidiarity—in an attempt to include other religious traditions and motivate all persons committed to a more just and peaceful social order

Reconstruction of the spin state

System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state reconstruction. Repeated incompatible observations represent a new generalized measurement. This idealized scheme will serve for analysis of future experiments in neutron and quantum optics.Comment: 4 pages, 1 figur

Quantum correlation games

A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of correlations, i.e. without reference to classical or quantum mechanics. Classical bi-matrix games are reproduced if the input states are classical and perfectly anti-correlated, that is, for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. For example, the Prisoners' Dilemma acquires a Nash equilibrium if both players apply a mixed strategy. It appears to be conceptually impossible to reproduce the properties of quantum correlation games within the framework of classical games

On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six

An analytic proof is given which shows that it is impossible to extend any triple of mutually unbiased (MU) product bases in dimension six by a single MU vector. Furthermore, the 16 states obtained by removing two orthogonal states from any MU product triple cannot figure in a (hypothetical) complete set of seven MU bases. These results follow from exploiting the structure of MU product bases in a novel fashion, and they are among the strongest ones obtained for MU bases in dimension six without recourse to computer algebra.Comment: 12 pages, identical to published versio

Minimal Informationally Complete Measurements for Pure States

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PSI-complete) POVM. We show that a measurement with 2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D outcomes. We also consider PSI-complete POVMs that have only rank-one POVM elements and construct an example with 3D-2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PSI-complete POVM is left open.Comment: 2 figures, submitted for the Asher Peres festschrif

PT-symmetry and its spontaneous breakdown explained by anti-linearity

The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed