Passive decoy state quantum key distribution: Closing the gap to perfect sources

We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present-day, non-ideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical post-processing. This allows to improve the effective signal statistics and achievable distance.Comment: 4 pages, 3 figures. State preparation correcte

Prevalence of vertebral fractures on chest radiographs of elderly African American and Caucasian women.

The prevalence of vertebral fractures on routine chest radiographs of elderly Caucasian women was only 1.3 times higher than in African American (AA) women, a difference considerably smaller than reported in population studies. AAs with medical problems may have higher risk of vertebral fractures than previously suspected.IntroductionEarlier studies noted a 1.9- to 3.7-fold higher prevalence of vertebral fractures in Caucasian (CA) compared to African American (AA) women. These studies, however, may have suffered from selection bias. We reported that among women referred for bone density testing, the prevalence of vertebral fractures in AA was the same as in CA women. Suspecting that the latter might have been due to a referral bias, we examined the racial difference in the prevalence of vertebra fractures on chest radiographs of patients seeking general medical care, not selected for osteoporosis.MethodsConsecutive chest radiographs (N = 1,200) of women over age 60 were evaluated using Genant's semi-quantitative method. Patients' race and the presence of diseases or medications associated with increased fracture risk were ascertained from the electronic medical records.ResultsAmong 1,011 women (76% AA) with usable radiographs, 11% had moderate or severe vertebral fractures. The prevalence of vertebral fractures was 10.3% in 773 AA and 13% in 238 CA women (p = 0.248 for difference between races). The lack of difference persisted after controlling for age, smoking, use of glucocorticoids, or presence of cancer, rheumatoid arthritis, organ transplantation, and end-stage renal disease. Among all subjects, CA women were more likely to be diagnosed and treated for osteoporosis (p <0.001).ConclusionAmong subjects seeking medical care, the difference in the prevalence of vertebral fractures between AA and CA women is smaller than previously suspected. Greater attention to the detection of vertebral fractures and the management of osteoporosis is warranted in AA women with medical problems

Quantum correlations from local amplitudes and the resolution of the Einstein-Podolsky-Rosen nonlocality puzzle

The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is resolved if the quantum correlations are calculated directly from local quantities which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes, and calculate an amplitude correlation function.Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that the measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently `nonlocal' effects like quantum teleportation and entanglement swapping are different from what is usually assumed. Bell type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples we discuss the quantum correlations of two-particle maximally entangled states and the three-particle GHZ entangled state.Comment: Std. Latex, 11 pages, 1 table. Prepared for presentation at the International Conference on Quantum Optics, ICQO'2000, Minsk, Belaru

Quantum complexities of ordered searching, sorting, and element distinctness

We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary comparisons for element distinctness. The previously best known lower bounds are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}), respectively. Our proofs are based on a weighted all-pairs inner product argument. In addition to our lower bound results, we give a quantum algorithm for ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster algorithm due to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some of the results have previously been presented at QIP '01. This paper subsumes the papers quant-ph/0009091 and quant-ph/000903

Quantum Cryptography Based on the Time--Energy Uncertainty Relation

A new cryptosystem based on the fundamental time--energy uncertainty relation is proposed. Such a cryptosystem can be implemented with both correlated photon pairs and single photon states.Comment: 5 pages, LaTex, no figure

Gravitational Lensing Signature of Long Cosmic Strings

The gravitational lensing by long, wiggly cosmic strings is shown to produce a large number of lensed images of a background source. In addition to pairs of images on either side of the string, a number of small images outline the string due to small-scale structure on the string. This image pattern could provide a highly distinctive signature of cosmic strings. Since the optical depth for multiple imaging of distant quasar sources by long strings may be comparable to that by galaxies, these image patterns should be clearly observable in the next generation of redshift surveys such as the Sloan Digital Sky Survey.Comment: 4 pages, revtex with 3 postscript figures include

Scaling Property of the global string in the radiation dominated universe

We investigate the evolution of the global string network in the radiation dominated universe by use of numerical simulations in 3+1 dimensions. We find that the global string network settles down to the scaling regime where the energy density of global strings, $\rho_{s}$, is given by $\rho_{s} = \xi \mu / t^2$ with $\mu$ the string tension per unit length and the scaling parameter, $\xi \sim (0.9-1.3)$, irrespective of the cosmic time. We also find that the loop distribution function can be fitted with that predicted by the so-called one scale model. Concretely, the number density, $n_{l}(t)$, of the loop with the length, $l$, is given by $n_{l}(t) = \nu/[t^{3/2} (l + \kappa t)^{5/2}]$ where $\nu \sim 0.0865$ and $\kappa$ is related with the Nambu-Goldstone(NG) boson radiation power from global strings, $P$, as $P = \kappa \mu$ with $\kappa \sim 0.535$. Therefore, the loop production function also scales and the typical scale of produced loops is nearly the horizon distance. Thus, the evolution of the global string network in the radiation dominated universe can be well described by the one scale model in contrast with that of the local string network.Comment: 18 pages, 9 figures, to appear in Phys. Rev.

A Comprehensive Archival Search for Counterparts to Ultra-Compact High Velocity Clouds: Five Local Volume Dwarf Galaxies

We report five Local Volume dwarf galaxies (two of which are presented here for the first time) uncovered during a comprehensive archival search for optical counterparts to ultra-compact high velocity clouds (UCHVCs). The UCHVC population of HI clouds are thought to be candidate gas-rich, low mass halos at the edge of the Local Group and beyond, but no comprehensive search for stellar counterparts to these systems has been presented. Careful visual inspection of all publicly available optical and ultraviolet imaging at the position of the UCHVCs revealed six blue, diffuse counterparts with a morphology consistent with a faint dwarf galaxy beyond the Local Group. Optical spectroscopy of all six candidate dwarf counterparts show that five have an H$\alpha$-derived velocity consistent with the coincident HI cloud, confirming their association, the sixth diffuse counterpart is likely a background object. The size and luminosity of the UCHVC dwarfs is consistent with other known Local Volume dwarf irregular galaxies. The gas fraction ($M_{HI}/M_{star}$) of the five dwarfs are generally consistent with that of dwarf irregular galaxies in the Local Volume, although ALFALFA-Dw1 (associated with ALFALFA UCHVC HVC274.68+74.70$-$123) has a very high $M_{HI}/M_{star}$$\sim$40. Despite the heterogenous nature of our search, we demonstrate that the current dwarf companions to UCHVCs are at the edge of detectability due to their low surface brightness, and that deeper searches are likely to find more stellar systems. If more sensitive searches do not reveal further stellar counterparts to UCHVCs, then the dearth of such systems around the Local Group may be in conflict with $\Lambda$CDM simulations.Comment: 18 pages, 4 tables, 4 figures, ApJ Accepte

Observing Long Cosmic Strings Through Gravitational Lensing

We consider the gravitational lensing produced by long cosmic strings formed in a GUT scale phase transition. We derive a formula for the deflection of photons which pass near the strings that reduces to an integral over the light cone projection of the string configuration plus constant terms which are not important for lensing. Our strings are produced by performing numerical simulations of cosmic string networks in flat, Minkowski space ignoring the effects of cosmological expansion. These strings have more small scale structure than those from an expanding universe simulation - fractal dimension 1.3 for Minkowski versus 1.1 for expanding - but share the same qualitative features. Lensing simulations show that for both point-like and extended objects, strings produce patterns unlike more traditional lenses, and, in particluar, the kinks in strings tend to generate demagnified images which reside close to the string. Thus lensing acts as a probe of the small scale structure of a string. Estimates of lensing probablity suggest that for string energy densities consistant with string seeded structure formation, on the order of tens of string lenses should be observed in the Sloan Digital Sky Survey quasar catalog. We propose a search strategy in which string lenses would be identified in the SDSS quasar survey, and the string nature of the lens can be confirmed by the observation of nearby high redshift galaxies which are also be lensed by the string.Comment: 24 pages revtex with 12 postscript firgure

Error threshold in optimal coding, numerical criteria and classes of universalities for complexity

The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size corrections proportional to the square root of the number of degrees. The response of the magnetization to the ferromagnetic couplings is maximal at the values of magnetization equal to half. We give several criteria of complexity and define different universality classes. According to our classification, at the lowest class of complexity are random graph, Markov Models and Hidden Markov Models. At the next level is Sherrington-Kirkpatrick spin glass, connected with neuron-network models. On a higher level are critical theories, spin glass phase of Random Energy Model, percolation, self organized criticality (SOC). The top level class involves HOT design, error threshold in optimal coding, language, and, maybe, financial market. Alive systems are also related with the last class. A concept of anti-resonance is suggested for the complex systems.Comment: 17 page