The quantum speed up as advanced knowledge of the solution

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple two line argument for this without having to describe the details of the search algorithm". The answer provided in this work is: "because any quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem". This empirical fact, unnoticed so far, holds for both quadratic and exponential speed ups and is theoretically justified in three steps: (i) once the physical representation is extended to the production of the problem on the part of the oracle and to the final measurement of the computer register, quantum computation is reduction on the solution of the problem under a relation representing problem-solution interdependence, (ii) the speed up is explained by a simple consideration of time symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution; this advanced knowledge of the solution reduces the size of the solution space to be explored by the algorithm, (iii) if I is the information acquired by measuring the content of the computer register at the end of the algorithm, the quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of I, which brings us to the initial statement.Comment: 23 pages, to be published in IJT

Cosmic rays 10Be biennal data and their relationship to aurorae and sunspots

The galactic cosmic ray (C.R.) variations which should give information on three dimensional aspects of the heliospheric magnetic fields and on the solar wind, which modulate their influx into the Solar System were studied. In order to decode the information from the C.R. series it is necessary to know the mechanisms through which the modulation is produced. It it clear that a balance of effects with sources at different heliospheric latitudes results in the modulated C.R. intensity. It is found that the modulation of 10Be in polar ice may be due to at least two main contributions: (1) negative and in phase with the Solar flare activity modulating the cosmic ray flux in Forbush-type decreases, and (2) positive in phase with the appearance of large wind streams situated at both polar coronal holes. It is found that the high heliolatitude activity is related to a stable periodicity of 11.1y whereas the low heliolatitude activity contributes to the wondering of the solar cycles

Cosmic ray secular variations in terrestrial records and aurorae

The rediscovery that the Sun and the solar wind can undergo important changes on historical time scales has brought into question the stability of the cyclic behavior of past time series of solar and solar-terrestrial origin. It was found by Vector Fourier analysis that the solar 11 year cycle is present in the series of 10Be, delta 180, in ice cores and of thermoluminescence (TL) in sea sediments during the last Millennia with a frequency modulation, related to the Sun behavior, as tested by comparison with the Sunspot number R sub z series. It was shown that the cyclogram of the series of yearly Aurorae from 1721 to 1979 linear-regression-corrected-for-R sub z is straight for the periodicity zeta=11,1y, which indicates that such periodicity is constant in time corresponding to the only line present in the 11y band. The maxima of this component appear at the same time together with the high speed solar wind streams taking place in coronal holes situated in high heliolatitudes. It is evidenced that the 11 year cycle has undergone frequency oscillations on a time scale of two centuries, although it is very difficult to determine the periodicities with high accuracy

A Monte Carlo Calculation of Atmospheric Muon and Neutrino Fluxes

Production of muons and neutrinos in cosmic ray interactions with the atmosphere has been investigated with a cascade simulation program based on Lund Monte Carlo programs. The resulting `conventional' muon and neutrino fluxes (from $\pi ,K$ decays) agree well with earlier calculations, whereas the improved charm particle treatment used in this study gives significantly lower `prompt' fluxes compared to earlier estimates. This implies better prospects for detecting very high energy neutrinos from cosmic sources.Comment: 4 pages, uuencoded and gziped ps-fil

Reply to Comment on "Quantum dense key distribution"

In this Reply we propose a modified security proof of the Quantum Dense Key Distribution protocol detecting also the eavesdropping attack proposed by Wojcik in his Comment.Comment: To appear on PRA with minor change

The 50% advanced information rule of the quantum algorithms

The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. Here we check that this 50% rule holds for the main quantum algorithms. In the structured problems, a classical algorithm with the advanced information, to identify the missing information should perform one function evaluation. The speed up is exponential since a classical algorithm without advanced information should perform an exponential number of function evaluations. In unstructured database search, a classical algorithm that knows in advance 50% of the n bits of the database location, to identify the n/2 missing bits should perform Order(2 power n/2) function evaluations. The speed up is quadratic since a classical algorithm without advanced information should perform Order(2 power n) function evaluations. The 50% rule identifies the problems solvable with a quantum sped up in an entirely classical way, in fact by comparing two classical algorithms, with and without the advanced information.Comment: 18 pages, submitted with minor changes to the International Journal of Theoretical Physic

Experimental noise-resistant Bell-inequality violations for polarization-entangled photons

We experimentally demonstrate that violations of Bell's inequalities for two-photon polarization-entangled states with colored noise are extremely robust, whereas this is not the case for states with white noise. Controlling the amount of noise by using the timing compensation scheme introduced by Kim et al. [Phys. Rev. A 67, 010301(R) (2003)], we have observed violations even for states with very high noise, in excellent agrement with the predictions of Cabello et al. [Phys. Rev. A 72, 052112 (2005)].Comment: REVTeX4, 5 pages, 4 figure