Using of small-scale quantum computers in cryptography with many-qubit entangled states

We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted through a quantum channel to the addressee, who applies a quantum computer tuned to realize the inverse unitary transformation decoding of the message. Different ways of eavesdropping are considered, and an estimate of the time needed for determining the secret unitary transformation is given. It is shown that using even small quantum computers can serve as a basis for very efficient cryptographic protocols. For a suggested cryptographic protocol, the time scale on which communication can be considered secure is exponential in the number of qubits in the entangled states and in the number of gates used to construct the quantum network

Microcurrent stimulation in the treatment of dry and wet macular degeneration

Purpose: To determine the safety and efficacy of the application of transcutaneous (transpalpebral) microcurrent stimulation to slow progression of dry and wet macular degeneration or improve vision in dry and wet macular degeneration. Methods: Seventeen patients aged between 67 and 95 years with an average age of 83 years were selected to participate in the study over a period of 3 months in two eye care centers. There were 25 eyes with dry age-related macular degeneration (DAMD) and six eyes with wet age-related macular degeneration (WAMD). Frequency-specific microcurrent stimulation was applied in a transpalpebral manner, using two programmable dual channel microcurrent units delivering pulsed microcurrent at 150 μA for 35 minutes once a week. The frequency pairs selected were based on targeting tissues, which are typically affected by the disease combined with frequencies that target disease processes. Early Treatment Diabetic Retinopathy Study or Snellen visual acuity (VA) was measured before and after each treatment session. All treatment was administered in a clinical setting. Results: Significant increases were seen in VA in DAMD (P=0.012, Wilcoxon one-sample test), but in WAMD, improvements did not reach statistical significance (P=0.059). In DAMD eyes, twice as many patients showed increase in VA (52%) compared to those showing dete-rioration (26%), with improvements being often sizeable, whereas deteriorations were usually very slight. In WAMD eyes, five of six (83%) patients showed an increase and none showed deterioration. Conclusion: The substantial changes observed over this period, combined with continued improvement for patients who continued treatment once a month, are encouraging for future studies. The changes observed indicate the potential efficacy of microcurrent to delay degeneration and possibly improve age-related macular degeneration, both wet and dry. However, this study has no control arm, so results should be treated with caution. Randomized double-blind controlled studies are needed to determine long-term effects

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.

Evolution of a global string network in a matter dominated universe

We evolve the network of global strings in the matter-dominated universe by means of numerical simulations. The existence of the scaling solution is confirmed as in the radiation-dominated universe but the scaling parameter $\xi$ takes a slightly smaller value, $\xi \simeq 0.6 \pm 0.1$, which is defined as $\xi = \rho_{s} t^{2} / \mu$ with $\rho_{s}$ the energy density of global strings and $\mu$ the string tension per unit length. The change of $\xi$ from the radiation to the matter-dominated universe is consistent with that obtained by Albrecht and Turok by use of the one-scale model. We also study the loop distribution function and find that it can be well fitted with that predicted by the one-scale model, where the number density $n_{l}(t)$ of the loop with the length $l$ is given by $n_{l}(t) = \nu/[t^2 (l + \kappa t)^2]$ with $\nu \sim 0.040$ and $\kappa \sim 0.48$. Thus, the evolution of the global string network in the matter-dominated universe can be well described by the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure

Relic Gravitational Waves and Their Detection

The range of expected amplitudes and spectral slopes of relic (squeezed) gravitational waves, predicted by theory and partially supported by observations, is within the reach of sensitive gravity-wave detectors. In the most favorable case, the detection of relic gravitational waves can be achieved by the cross-correlation of outputs of the initial laser interferometers in LIGO, VIRGO, GEO600. In the more realistic case, the sensitivity of advanced ground-based and space-based laser interferometers will be needed. The specific statistical signature of relic gravitational waves, associated with the phenomenon of squeezing, is a potential reserve for further improvement of the signal to noise ratio.Comment: 25 pages, 9 figures included, revtex. Based on a talk given at "Gyros, Clocks, and Interferometers: Testing General Relativity in Space" (Germany, August 99

Affine Constellations Without Mutually Unbiased Counterparts

It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.Comment: 8 page

Test of Bell's Inequality using the Spin Filter Effect in Ferromagnetic Semiconductor Micro-structures

A theoretical proposal for testing Bell's inequality in mesoscopic systems is presented. We show that the entanglement of two electron spins can be detected in the spin filter effect in the mesoscopic semiconductor / ferromagnetic semiconductor / semiconductor junction. The current-current correlation function is calculated by use of the quantum scattering theory and we compare it with the local hidden variable theory. We also discuss the influence of an imperfect spin filter and derive the condition to see the violation of Bell's inequality experimentally.Comment: 6 pages, 4 figures, submitted to J. Phys. Soc. Jp

Entanglement Creation Using Quantum Interrogation

We present some applications of high efficiency quantum interrogation ("interaction free measurement") for the creation of entangled states of separate atoms and of separate photons. The quantum interrogation of a quantum object in a superposition of object-in and object-out leaves the object and probe in an entangled state. The probe can then be further entangled with other objects in subsequent quantum interrogations. By then projecting out those cases were the probe is left in a particular final state, the quantum objects can themselves be left in various entangled states. In this way we show how to generate two-, three-, and higher qubit entanglement between atoms and between photons. The effect of finite efficiency for the quantum interrogation is delineated for the various schemes.Comment: 7 pages, 13 figures, Submitted to PR

Violation of Bell inequalities by photons more than 10 km apart

A Franson-type test of Bell inequalities by photons 10.9 km apart is presented. Energy-time entangled photon-pairs are measured using two-channel analyzers, leading to a violation of the inequalities by 16 standard deviations without subtracting accidental coincidences. Subtracting them, a 2-photon interference visibility of 95.5% is observed, demonstrating that distances up to 10 km have no significant effect on entanglement. This sets quantum cryptography with photon pairs as a practical competitor to the schemes based on weak pulses.Comment: 4 pages, REVTeX, 2 postscript figures include