Generating optimal states for a homodyne Bell test

Published versio

Fixed Points of Generalized Contractive Multi-valued Mappings

In a recent paper N. Mizoguchi and W. Takahashi gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from their paper (J. Math. Anal. Appl. 141 (1989), 177-188)

A two-parameter control for contractive-like multivalued mappings

We propose a general approach to defining a contractive-like multivalued mappings $F$ which avoids any use of the Hausdorff distance between the sets $F(x)$ and $F(y)$. Various fixed point theorems are proved under a two-parameter control of the distance function $d_{F}(x)=dist(x,F(x))$ between a point $x \in X$ and the value F(x) \ss X. Here, both parameters are numerical functions. The first one \a\,:[0,+\i)\rightarrow [1,+\i) controls the distance between $x$ and some appropriate point $y \in F(x)$ in comparison with $d_{F}(x)$, whereas the second one \b\,:[0,+\i)\rightarrow [0,1) estimates $d_{F}(y)$ with respect to $d(x,y)$. It appears that the well harmonized relations between \a and \b are sufficient for the existence of fixed points of $F$. Our results generalize several known fixed-point theorems

Long term changes in the upper stratospheric ozone at Syowa, Antarctica

第2回極域科学シンポジウム/第35回極域宙空圏シンポジウム 11月15日（火） 国立極地研究所 2階大会議

On a Conjecture of S. Reich

Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings

Jet and Tropopause Products for Analysis and Characterization (JETPAC)

This suite of IDL programs provides identification and comprehensive characterization of the dynamical features of the jet streams in the upper troposphere, the lower stratospheric polar night jet, and the tropopause. The output of this software not only provides comprehensive information on the jets and tropopause, but also gives this information in a form that facilitates studies of observations in relation to the jets and tropopauses

Quantum-circuit guide to optical and atomic interferometry

Atomic (qubit) and optical or microwave (modal) phase-estimation protocols are placed on the same footing in terms of quantum-circuit diagrams. Circuit equivalences are used to demonstrate the equivalence of protocols that achieve the Heisenberg limit by employing entangled superpositions of Fock states, such as N00N states. The key equivalences are those that disentangle a circuit so that phase information is written exclusively on a mode or modes or on a qubit. The Fock-state-superposition phase-estimation circuits are converted to use entangled coherent-state superpositions; the resulting protocols are more amenable to realization in the lab, particularly in a qubit/cavity setting at microwave frequencies.Comment: To appear in Optics Communications special issue in memory of Krzysztof Wodkiewic

Bloch Equations and Completely Positive Maps

The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and colored stochastic noise.Comment: Talk given at the Conference "Quantum Challenges", Falenty, Poland, September 4-7, 2003. 21 pages, 3 figure