Quantum-state filtering applied to the discrimination of Boolean functions

Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, {|\psi_{1} >, ..., |\psi_{N} >}, for distinguishing |\psi_1 > from the set {|\psi_2 >, ..., |\psi_N >} and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased functions. The algorithm is probabilistic, it fails sometimes but when it does it lets us know that it did. Our approach can be considered as a generalization of the Deutsch-Jozsa algorithm that was developed for the discrimination of balanced and constant Boolean functions.Comment: 8 page

Plexcitons: Dirac points and topological modes

Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. We consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional bandstructure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. These Dirac cones may open up in energy by simultaneously interfacing the metal with a magneto-optical layer and subjecting the whole system to a perpendicular magnetic field. The resulting energy gap becomes populated with topologically protected one-way modes which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter as well as of novel ways to direct energy flow at the nanoscale

Effects of geometric anisotropy on local field distribution: Ewald-Kornfeld formulation

We have applied the Ewald-Kornfeld formulation to a tetragonal lattice of point dipoles, in an attempt to examine the effects of geometric anisotropy on the local field distribution. The various problems encountered in the computation of the conditionally convergent summation of the near field are addressed and the methods of overcoming them are discussed. The results show that the geometric anisotropy has a significant impact on the local field distribution. The change in the local field can lead to a generalized Clausius-Mossotti equation for the anisotropic case.Comment: Accepted for publications, Journal of Physics: Condensed Matte

Optimal Bidding Strategies for Simultaneous Vickrey Auctions with Perfect Substitutes

We derive optimal bidding strategies for a global bidder who participates in multiple, simultaneous second-price auctions with perfect substitutes. We prove that, if everyone else bids locally in a single auction, the global bidder should always place non-zero bids in all available auctions, provided there are no budget constraints. With a budget, however, the optimal strategy is to bid locally if this budget is equal or less than the valuation. Furthermore, for a wide range of valuation distributions, we prove that the problem of finding the optimal bids reduces to two dimensions if all auctions are identical. Moreoever, we address markets with both sequential and simultaneous auctions, non-identical auctions, and the allocative efficiency of the market. Finally, by combining analystical and simulation results, we analyse equilibrium strategies in case of several global bidders. However, a stable solution is then only found if there are local bidders as well

Reconstituted high-density lipoproteins promote wound repair and blood flow recovery in response to ischemia in aged mice

Background: The average population age is increasing and the incidence of age-related vascular complications is rising in parallel. Impaired wound healing and disordered ischemia-mediated angiogenesis are key contributors to age-impaired vascular complications that can lead to amputation. High-density lipoproteins (HDL) have vasculo-protective properties and augment ischemia-driven angiogenesis in young animals. We aimed to determine the effect of reconstituted HDL (rHDL) on aged mice in a murine wound healing model and the hindlimb ischemia (HLI) model. Methods: Murine wound healing model—24-month-old aged mice received topical application of rHDL (50 μg/wound/ day) or PBS (vehicle control) for 10 days following wounding. Murine HLI model—Femoral artery ligation was performed on 24-month-old mice. Mice received rHDL (40 mg/kg) or PBS, intravenously, on alternate days, 1 week pre-surgery and up to 21 days post ligation. For both models, blood flow perfusion was determined using laser Doppler perfusion imaging. Mice were sacrificed at 10 (wound healing) or 21 (HLI) days post-surgery and tissues were collected for histological and gene analyses. Results: Daily topical application of rHDL increased the rate of wound closure by Day 7 post-wounding (25 %, p < 0.05). Wound blood perfusion, a marker of angiogenesis, was elevated in rHDL treated wounds (Days 4–10 by 22–25 %, p < 0. 05). In addition, rHDL increased wound capillary density by 52.6 %. In the HLI model, rHDL infusions augmented blood flow recovery in ischemic limbs (Day 18 by 50 % and Day 21 by 88 %, p < 0.05) and prevented tissue necrosis and toe loss. Assessment of capillary density in ischemic hindlimb sections found a 90 % increase in rHDL infused animals. In vitro studies in fibroblasts isolated from aged mice found that incubation with rHDL was able to significantly increase the key pro-angiogenic mediator vascular endothelial growth factor (VEGF) protein (25 %, p < 0.05). Conclusion: rHDL can promote wound healing and wound angiogenesis, and blood flow recovery in response to ischemia in aged mice. Mechanistically, this is likely to be via an increase in VEGF. This highlights a potential role for HDL in the therapeutic modulation of age-impaired vascular complications

Clustering of childhood leukaemia in Hong Kong: association with the childhood peak and common acute lymphoblastic leukaemia and with population mixing.

Incidence data of childhood leukaemia (CL) in Hong Kong (1984-90) have been analysed for evidence of variation between small areas. All cases (n=261) were classified by morphological cell type, with the majority (n=205) being acute lymphoblastic leukaemia (ALL), and haematological review has permitted immunophenotypic classification for 73% of these. The data have been examined for evidence of spatial clustering within small census areas (TPUs) and for association with population mixing, with attention focused on those subgroups (especially the childhood peak of ALL--taken here to be diagnoses in children from 24 months up to the seventh birthday--and common ALL) which, it has been hypothesized, may be caused by unusual patterns of exposure and response to common infections. For the whole of Hong Kong, there was evidence of spatial clustering of ALL at ages 0-4 years (P = 0.09) and in the childhood peak (P<0.05). When these analyses were restricted to TPUs where extreme population mixing may have occurred, overall incidence was elevated and significant evidence of clustering was found for ALL (P<0.007) at these ages and for the common ALL in the childhood peak (P = 0.032). Replication of the analyses for subsets of leukaemia that were not dominated by the childhood peak of ALL found no evidence of clustering. This is the first investigation of an association between population mixing and childhood leukaemia in Asia and the first to include clustering and to consider particular subsets. The results are supportive of the 'infectious' aetiology hypothesis for subsets of childhood leukaemia, specifically common ALL in the childhood peak

Distinguishing between optical coherent states with imperfect detection

Several proposed techniques for distinguishing between optical coherent states are analyzed under a physically realistic model of photodetection. Quantum error probabilities are derived for the Kennedy receiver, the Dolinar receiver and the unitary rotation scheme proposed by Sasaki and Hirota for sub-unity detector efficiency. Monte carlo simulations are performed to assess the effects of detector dark counts, dead time, signal processing bandwidth and phase noise in the communication channel. The feedback strategy employed by the Dolinar receiver is found to achieve the Helstrom bound for sub-unity detection efficiency and to provide robustness to these other detector imperfections making it more attractive for laboratory implementation than previously believed