Research and development activities in unified control-structure modeling and design

Results of work sponsored by JPL and other organizations to develop a unified control/structures modeling and design capability for large space structures is presented. Recent analytical results are presented to demonstrate the significant interdependence between structural and control properties. A new design methodology is suggested in which the structure, material properties, dynamic model and control design are all optimized simultaneously. The development of a methodology for global design optimization is recommended as a long term goal. It is suggested that this methodology should be incorporated into computer aided engineering programs, which eventually will be supplemented by an expert system to aid design optimization. Recommendations are also presented for near term research activities at JPL. The key recommendation is to continue the development of integrated dynamic modeling/control design techniques, with special attention given to the development of structural models specially tailored to support design

Approximate Randomization of Quantum States With Fewer Bits of Key

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approximately randomizing map for d-dimensional states. Finally, we discuss the optimality of these schemes via connections to different notions of pseudorandomness, and give a new lower bound for small epsilon.Comment: 18 pages, Quantum Computing Back Action, IIT Kanpur, March 2006, volume 864 of AIP Conference Proceedings, pages 18--36. Springer, New Yor

Aspects of nonlocality in atom-photon interactions in a cavity

We investigate a Bell-type inequality for probabilities of detected atoms formulated using atom-photon interactions in a cavity. We consider decoherence brought about by both atomic decay, as well as cavity photon loss, and study its quantitative action in diminishing the atom-field and the resultant atom-atom secondary correlations. We show that the effects of decoherence on nonlocality can be observed in a controlled manner in actual experiments involving the micromaser and also the microlaser.Comment: 9 pages, 3 .eps figures, Revtex. Revised version with details of calculations and more result

The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime

We compute the effect of Landau-level-mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the lowest relative angular momentum channel. The renormalization of the two-body pseudopotentials also shows interesting structure. We comment on the implications for the $\nu=5/2$ fractional quantum Hall state

Recognizing well-parenthesized expressions in the streaming model

Motivated by a concrete problem and with the goal of understanding the sense in which the complexity of streaming algorithms is related to the complexity of formal languages, we investigate the problem Dyck(s) of checking matching parentheses, with $s$ different types of parenthesis. We present a one-pass randomized streaming algorithm for Dyck(2) with space \Order(\sqrt{n}\log n), time per letter \polylog (n), and one-sided error. We prove that this one-pass algorithm is optimal, up to a \polylog n factor, even when two-sided error is allowed. For the lower bound, we prove a direct sum result on hard instances by following the "information cost" approach, but with a few twists. Indeed, we play a subtle game between public and private coins. This mixture between public and private coins results from a balancing act between the direct sum result and a combinatorial lower bound for the base case. Surprisingly, the space requirement shrinks drastically if we have access to the input stream in reverse. We present a two-pass randomized streaming algorithm for Dyck(2) with space \Order((\log n)^2), time \polylog (n) and one-sided error, where the second pass is in the reverse direction. Both algorithms can be extended to Dyck(s) since this problem is reducible to Dyck(2) for a suitable notion of reduction in the streaming model.Comment: 20 pages, 5 figure

Multi-channel Kondo Models in non-Abelian Quantum Hall Droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a $k$-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction $\nu=2+k/(k+2)$ or its particle-hole conjugate at $\nu=2+2/(k+2)$. The $k$-channel Kondo model is channel isotropic even without fine tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of $k=2$, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction $\nu=5/2$.Comment: 4 pages, 1 figure; references updated, version to appear in PR