Decoherence Functional and Inhomogeneities in the Early Universe

We investigate the quantum to classical transition of small inhomogeneous fluctuations in the early Universe using the decoherence functional of Gell-Mann and Hartle. We study two types of coarse graining; one due to coarse graining the value of the scalar field and the other due to summing over an environment. We compare the results with a previous study using an environment and the off-diagonal rule proposed by Zurek. We show that the two methods give different results.Comment: 15 pages in plain te

The Least Action Principle And The Spin Of Galaxies In The Local Group

Using Peebles' least action principle, we determine trajectories for the galaxies in the Local Group and the more massive galaxies in the Local Neighbourhood. We deduce the resulting angular momentum for the whole of the Local Group and study the tidal force acting on the Local Group and its galaxies. Although Andromeda and the Milky Way dominate the tidal force acting on each other during the present epoch, we show that there is a transition time at $z\approx 1$ before which the tidal force is dominated by galaxies outside the Local Group in each case. This shows that the Local Group can not be considered as an isolated system as far as the tidal forces are concerned. We integrate the tidal torques acting on the Milky Way and Andromeda and derive their spin angular momenta, obtaining results which are comparable with observation.Comment: 16 pages (5 figures available on request), plain TeX, IoA-93-01-AM

Resilient Quantum Computation: Error Models and Thresholds

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.Comment: 19 pages in RevTex, many figures, the paper is also avalaible at http://qso.lanl.gov/qc

Discord and quantum computational resources

Discordant states appear in a large number of quantum phenomena and seem to be a good indicator of divergence from classicality. While there is evidence that they are essential for a quantum algorithm to have an advantage over a classical one, their precise role is unclear. We examine the role of discord in quantum algorithms using the paradigmatic framework of `restricted distributed quantum gates' and show that manipulating discordant states using local operations has an associated cost in terms of entanglement and communication resources. Changing discord reduces the total correlations and reversible operations on discordant states usually require non-local resources. Discord alone is, however, not enough to determine the need for entanglement. A more general type of similar quantities, which we call K-discord, is introduced as a further constraint on the kinds of operations that can be performed without entanglement resources.Comment: Closer to published versio