Retrodiction of Generalised Measurement Outcomes

If a generalised measurement is performed on a quantum system and we do not know the outcome, are we able to retrodict it with a second measurement? We obtain a necessary and sufficient condition for perfect retrodiction of the outcome of a known generalised measurement, given the final state, for an arbitrary initial state. From this, we deduce that, when the input and output Hilbert spaces have equal (finite) dimension, it is impossible to perfectly retrodict the outcome of any fine-grained measurement (where each POVM element corresponds to a single Kraus operator) for all initial states unless the measurement is unitarily equivalent to a projective measurement. It also enables us to show that every POVM can be realised in such a way that perfect outcome retrodiction is possible for an arbitrary initial state when the number of outcomes does not exceed the output Hilbert space dimension. We then consider the situation where the initial state is not arbitrary, though it may be entangled, and describe the conditions under which unambiguous outcome retrodiction is possible for a fine-grained generalised measurement. We find that this is possible for some state if the Kraus operators are linearly independent. This condition is also necessary when the Kraus operators are non-singular. From this, we deduce that every trace-preserving quantum operation is associated with a generalised measurement whose outcome is unambiguously retrodictable for some initial state, and also that a set of unitary operators can be unambiguously discriminated iff they are linearly independent. We then examine the issue of unambiguous outcome retrodiction without entanglement. This has important connections with the theory of locally linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review

Supersymmetric codimension-two branes and U(1)_R mediation in 6D gauged supergravity

We construct a consistent supersymmetric action for brane chiral and vector multiplets in a six-dimensional chiral gauged supergravity. A nonzero brane tension can be accommodated by allowing for a brane-localized Fayet-Iliopoulos term proportional to the brane tension. When the brane chiral multiplet is charged under the bulk U(1)_R, we obtain a nontrivial coupling to the extra component of the U(1)_R gauge field strength as well as a singular scalar self-interaction term. Dimensionally reducing to 4D on a football supersymmetric solution, we discuss the implication of such interactions for obtaining the U(1)_R D-term in the 4D effective supergravity. By assuming the bulk gaugino condensates and nonzero brane F- and/or D-term for the uplifting potential, we have all the moduli stabilized with a vanishing cosmological constant. The brane scalar with nonzero R charge then gets a soft mass of order the gravitino mass. The overall sign of the soft mass squared depends on the sign of the R charge as well as whether the brane F- or D-term dominates.Comment: 28 pages, no figures, version to appear in JHE

Family Symmetry, Gravity, and the Strong CP Problem

We show how in a class of models Peccei--Quinn symmetry can be realized as an automatic consequence of a gauged $U(1)$ family symmetry. These models provide a solution to the strong CP problem either via a massless $u$--quark or via the DFSZ invisible axion. The local family symmetry protects against potentially large corrections to $\overline{\theta}$ induced by quantum gravitational effects. In a supersymmetric extension, the `$\mu$--problem' is shown to have a natural solution in the context of gravitationally induced operators. We also present a plausible mechanism which can explain the inter--generational mass hierarchy in such a context.Comment: BA-92-79, 14 pages, in LaTeX, no figure

Diagonalization of the neutralino mass matrix and boson-neutralino interaction

We analyze a connection between neutralino mass sign, parity and structure of the neutralino-boson interaction. Correct calculation of spin-dependent and spin-independent contributions to neutralino-nuclear scattering should consider this connection. A convenient diagonalization procedure, based on the exponetial parametrization of unitary matrix, is suggested.Comment: 21 pages, RevTex

Nontrival Cosmological Constant in Brane Worlds with Unorthodox Lagrangians

In self-tuning brane-world models with extra dimensions, large contributions to the cosmological constant are absorbed into the curvature of extra dimensions and consistent with flat 4d geometry. In models with conventional Lagrangians fine-tuning is needed nevertheless to ensure a finite effective Planck mass. Here, we consider a class of models with non conventional Lagrangian in which known problems can be avoided. Unfortunately these models are found to suffer from tachyonic instabilities. An attempt to cure these instabilities leads to the prediction of a positive cosmological constant, which in turn needs a fine-tuning to be consistent with observations.Comment: 17 pages, 1 figur

Multiscale Gaussian graphical models and algorithms for large-scale inference

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 119-123).Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale tree-structured graphs have attracted much attention for their computational efficiency as well as their ability to capture long-range correlations. However, tree models have limited modeling power that may lead to blocky artifacts. Previous works on extending trees to pyramidal structures resorted to computationally expensive methods to get solutions due to the resulting model complexity. In this thesis, we propose a pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve large-scale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although the graph has many cycles, its hierarchical structure enables us to develop a class of fast algorithms in the spirit of multipole methods. The algorithms operate by guiding far-apart nodes to communicate through coarser scales and considering only local interactions at finer scales. The consistent stochastic structure of the pyramidal graph provides great flexibilities in designing and analyzing inference algorithms. Based on emerging techniques for inference on Gaussian graphical models, we propose several different inference algorithms to compute not only the optimal estimates but also approximate error variances as well. In addition, we consider the problem of rapidly updating the estimates based on some new local information, and develop a re-estimation algorithm on the pyramidal graph. Simulation results show that this algorithm can be applied to reconstruct discontinuities blurred during the estimation process or to update the estimates to incorporate a new set of measurements introduced in a local region.by Myung Jin Choi.S.M

A study of the currency management for foreign investments of Korean insurance companies

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 74).The Korean insurance industry has rapidly grown over the past decade, and at the same time the asset size of Korean insurance companies increases very fast. So the effective and scientific asset management becomes very essential for these companies to stay profitable. Korean insurance companies are also expanding their business platforms abroad including emerging countries, and consequently the appropriate currency management becomes a very important issue in asset management. In this paper, various hedging instruments for managing currency risk were reviewed with the focus on Korean specific financial market conditions, and the researches on the optimum hedge ratio of foreign investments were also discussed. Based on the practice of leading companies and the academic approach of the currency management, I suggested the effective currency management strategy for foreign investments of Korean insurance companies.by Sung-Jin Choi.S.M