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Optical quantum communication utilizing satellite platforms has the potential to extend the reach of quantum key distribution (QKD) from terrestrial limits of ~200 km to global scales. We have developed a thorough numerical simulation using realistic simulated orbits and incorporating the effects of pointing error, diffraction, atmosphere and telescope design, to obtain estimates of the loss and background noise which a satellite-based system would experience. Combining with quantum optics simulations of sources and detection, we determine the length of secure key for QKD, as well as entanglement visibility and achievable distances for fundamental experiments. We analyze the performance of a low Earth orbit (LEO) satellite for downlink and uplink scenarios of the quantum optical signals. We argue that the advantages of locating the quantum source on the ground justify a greater scientific interest in an uplink as compared to a downlink. An uplink with a ground transmitter of at least 25 cm diameter and a 30 cm receiver telescope on the satellite could be used to successfully perform QKD multiple times per week with either an entangled photon source or with a weak coherent pulse source, as well as perform long-distance Bell tests and quantum teleportation. Our model helps to resolve important design considerations such as operating wavelength, type and specifications of sources and detectors, telescope designs, specific orbits and ground station locations, in view of anticipated overall system performance.

We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to correct for one bit errors which either preexisted or occurred in course of operation. The logical operations we consider allow one to cary out the vast majority of the steps in the quantum factoring algorithm. Thus, our results help bring quantum factoring and other quantum computations closer to reality, 5 pages in LaTex, 6 figures, submitted to Physical Review Letters, (May 12, 1996), the paper is also avalaible at http://qso.lanl.gov/qc/

One main problem for the future of practial quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories and quantum channels require gates with asymptotically zero error to store or transmit an input quantum state for arbitrarily long times or distances with fixed error. This report gives a method which has the property that to store or transmit a qubit with maximum error {epsilon} requires gates with errors at most {ital c}{epsilon} and storage or channel elements with error at most {epsilon}, independent of how long we wish to store the state or how far we wish to transmit it. The method relies on using concatenated quantum codes and hierarchically implemented recovery operations. The overhead of the method is polynomial in the time of storage or the distance of the transmission. Rigorous and heuristic lower bounds for the constant {ital c} are given.

Assumptions useful for fault tolerant quantum computing are stated and briefly discussed. We focus on assumptions related to properties of the computational system. The strongest form of the assumptions seems to be sufficient for achieving highly fault tolerant quantum computation. We discuss weakenings which are also likely to suffice.

We analyze a system consisting of an oscillator coupled to a field. With the field traced out as an environment, the oscillator loses coherence on a very short {\it decoherence timescale}; but, on a much longer {\it relaxation timescale}, predictably evolves into a unique, pure (ground) state. This example of {\it re-coherence} has interesting implications both for the interpretation of quantum theory and for the loss of information during black hole evaporation. We examine these implications by investigating the intermediate and final states of the quantum field, treated as an open system coupled to an unobserved oscillator.

The application of concatenated codes to fault tolerant quantum computing is discussed. We have previously shown that for quantum memories and quantum communication, a state can be transmitted with error {epsilon} provided each gate has error at most c{epsilon}. We show how this can be used with Shor`s fault tolerant operations to reduce the accuracy requirements when maintaining states not currently participating in the computation. Viewing Shor`s fault tolerant operations as a method for reducing the error of operations, we give a concatenated implementation which promises to propagate the reduction hierarchically. This has the potential of reducing the accuracy requirements in long computations.

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\sim \exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in $L$ ($\sim L^2$). This enormous speed-up is possible in principle because quantum computation can simultaneously follow all of the paths corresponding to the distinct classical inputs, obtaining the solution as a result of coherent quantum interference between the alternatives. Hence, a quantum computer is sophisticated interference device, and it is essential for its quantum state to remain coherent in the course of the operation. In this report we investigate the effect of decoherence on the quantum factorization algorithm and establish an upper bound on a ``quantum factorizable'' $L$ based on the decoherence suffered per operational step., 7 pages,LaTex + 2 postcript figures in a uuencoded file

We investigate the stability of the extremal black p-brane which contains a n-form and a dilaton. We show that the instability due to the s-mode, which was present in the uncharged and non-extremal p-brane, disappears in the extreme case. This is shown to be consistent with an entropy argument which shows that the zero entropy of the extremal black hole is approached more rapidly than the zero entropy of the black p-brane, which would mean an instability would violate the second law of thermodynamics.

Peebles has suggested an interesting method to trace back in time positions of galaxies called the least action method. This method applied on the Local Group galaxies seems to indicate that we live in an Ω≊0.1 Universe. We have studied a CDM N‐body simulation with Ω=0.2 and H=50 km s−1/Mpc and compare trajectories traced back from the Least Action Principle and the center of mass of the particle forming CDM halos. We have shown that the agreement between these set of trajectories is at best qualitative. We have also shown that the line of sight peculiar velocities are underestimated. This discrepancy is due to orphans, CDM particles which do not end up in halos. By varying the density parameter Ω in the least action principle we show that using this method we would underestimate the density of the Universe by a factor of 4–5.

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 meters. In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ${\sim} 10^{-20}$ meters, up to that of hundreds of kilometers. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into Space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable., 34 pages, 9 figures. Journal version, modified to respond to numerous suggestions

It is argued that the observed thermodynamic arrow of time must arise from the boundary conditions of the Universe. We analyze the consequences of the no-boundary proposal, the only reasonably complete set of boundary conditions that has been put forward. We study perturbations of a Friedmann model containing a massive scalar field, but our results should be independent of the details of the matter content. We find that gravitational wave perturbations have an amplitude that remains in the linear regime at all times and is roughly time symmetric about the time of maximum expansion. Thus gravitational wave perturbations do not give rise to an arrow of time. However, density perturbations behave very differently. They are small at one end of the Universe's history, but grow larger and become nonlinear as the Universe gets larger. Contrary to an earlier claim, the density perturbations do not get small again at the other end of the Universe's history. They therefore give rise to a thermodynamic arrow of time that points in a constant direction while the Universe expands and contracts again. The arrow of time does not reverse at the point of maximum expansion. One has to appeal to the weak anthropic principle to explain why we observe the thermodynamic arrow to agree with the cosmological arrow, the direction of time in which the Universe is expanding.

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., 16 pages (5 figures available on request), plain TeX, IoA-93-01-AMD

We investigate the evolution of small perturbations around black strings and branes which are low energy solutions of string theory. For simplicity we focus attention on the zero charge case and show that there are unstable modes for a range of time frequency and wavelength in the extra $10-D$ dimensions. These perturbations can be stabililized if the extra dimensions are compactified to a scale smaller than the minimum wavelength for which instability occurs and thus will not affect large astrophysical black holes in four dimensions. We comment on the implications of this result for the Cosmic Censorship Hypothesis., 11 pages plain TeX, 2 figures (not included), EFI-93-02 (TeX corrected)

We investigate the time neutral formulation of quantum cosmology of Gell-Mann and Hartle. In particular we study the proposal discussed by them that our Universe corresponds to the time symmetric decoherence functional with initial and final density matrix of low entropy. We show that our Universe does not correspond to this proposal by investigating the behaviour of small inhomogeneous perturbations around a Friedman-Robertson-Walker model. These perturbations cannot be time symmetric if they were small at the Big Bang., Comment: 9 pages + 1 Figure, Tex

We comment on the range of the lapse integration in quantum cosmology. We show by an explicit example that the range of the gauge-fixed lapse in the path integral need not be invariant under lapse rescalings in the action. In particular, the range appropriate for recovering a Green's function of the Wheeler-DeWitt operator may be smaller than semi-infinite. The importance of a careful treatment of the singularities in the lapse integral is emphasized.

We report on the first real-time implementation of a quantum key distribution (QKD) system using entangled photon pairs that are sent over two free-space optical telescope links. The entangled photon pairs are produced with a type-II spontaneous parametric down-conversion source placed in a central, potentially untrusted, location. The two free-space links cover a distance of 435 m and 1,325 m respectively, producing a total separation of 1,575 m. The system relies on passive polarization analysis units, GPS timing receivers for synchronization, and custom written software to perform the complete QKD protocol including error correction and privacy amplification. Over 6.5 hours during the night, we observed an average raw key generation rate of 565 bits/s, an average quantum bit error rate (QBER) of 4.92%, and an average secure key generation rate of 85 bits/s., Comment: v2: Revised paper based on referee report, primarily in the Security assumption section and towards the end of the Experimental implementation section. 14 pages, 5 figures, higher resolution images will be available in the published article. v1: 13 pages, 5 figures, higher resolution images will be available in the published article

Every 18 months the number of transistors that can be packed onto a typical computer chip doubles. This is Moore's law – an empirical demonstration of our ingenuity to develop faster computers. Moore's law has held for the last 50 years, and if it holds for another 10 to 20 years then we will have created transistors that are the size of atoms. At this scale the classical laws of physics break down and are replaced by quantum mechanics.

Preface to Quantum coherence and decoherence. Proceedings of the ITP Conference in Santa Barbara, 15 to 18 December 1996 published by the Royal Society of London.

Peebles has suggested an interesting method to trace back in time positions of galaxies called the least action method. This method applied on the Local Group galaxies seems to indicate that we live in an $\Omega\approx 0.1$ Universe. We have studied a CDM N-body simulation with $\Omega=0.2$ and $H=50 kms^{-1}/Mpc$ and compare trajectories traced back from the Least Action Principle and the center of mass of the particle forming CDM halos. We show that the agreement between these set of trajectories is at best qualitative. We also show that the line of sight peculiar velocities are underestimated. This discrepancy is due to orphans, CDM particles which do not end up in halos. By varying the density parameter $\Omega$ in the least action principle we show that using this method we would underestimate the density of the Universe by a factor of 4-5.

The wave function of the Universe defined by the Hartle-Hawking proposal is studied for two minisuperspace models, the Friedmann-Robertson-Walker universe with a massive scalar field and the anisotropic Kantowski-Sachs cosmology. Solutions of the Wheeler-DeWitt equation are evaluated numerically. We also examine the trajectories to which these correspond in the classical limit. Attention is focused on the fact that most classical trajectories recollapse to a singularity. They will add an oscillatory component to the wave function in the region of small three-volume where it is predominantly exponential. They will thus modify the original boundary conditions. The Kantowski-Sachs universes generically evolve from isotropy during expansion to increasing anisotropy during recollapse, ending as a black-hole interior. We comment, therefore, on the arrow of time naturally induced by the Hartle-Hawking proposal.

Path integrals of matter fields on non-trivial euclidean background manifolds are investigated. Wave functions of fields on a surface which divides a manifold in two disjoint parts, are introduced. We derive two assumptions of thermofield dynamics: the insertion of the “fictitious” system and the “vacuum” |0(β)〉. Other manifolds, well known from quantum field theory in curved spacetime are studied; the euclidean sections of the Rindler wedge, Schwarzschild and de Sitter space. We show that the mixed state perceived by an observer in one of these backgrounds is of the same origin as the one in the finite temperature case.

We evaluate the wave function of the universe for a de Sitter minisuperspace with inhomogeneous matter perturbations from a massive scalar field. From the Wheeler-DeWitt equation, we derive Schrodinger equations for the matter modes. We show that the matter part of the Hartle-Hawking wave function is the euclidean vacuum state of quantum field theory in curved spacetime.

We show that the Schwarzschild black hole extended to five dimensions by the addition of an extra dimension is stable against linearized perturbations of the metric; thus the topology of the horizon can be thought of as an extra black-hole hair.

The Euclidian Einstein equations with a cosmological constant and a conformally coupled scalar field are solved, taking the metric to be of the Robertson-Walker type. In the case Lambda = 0, solutions are found which represent a wormhole connecting two asymptotically flat Euclidian regions. In the case Lambda greater than 0, the solutions represent tunneling from a small Tolman-like universe to a large Robertson-Walker universe.

The motive for the introduction of a fictitious field and the vacuum in thermo field dynamics is derived from Euclidean path integrals. We show that the occurrence of a fictitious system, both in the theory of Umezawa and Takahashi at finite temperature and the one of Israel for black hole backgrounds, can be related to the geometry of the Euclidean section of their spacetime.

We solve the Euclidean Einstein equations with three-index antisymmetric and two-index antisymmetric (electromagnetic) tensors for monopole configurations on a space with three-surfaces of topology {ital S}{sup 1}{times}{ital S}{sup 2} and describe wormhole solutions. We show that these wormholes and the one of Giddings and Strominger, Hawking, Halliwell and Laflamme, and Myers can be obtained by slicing five-dimensional spaces with horizons.

Little closed universes can branch off from our nearly flat region of spacetime. This leads to an extra degree of uncertainty, over and above that normally associate with quantum field theory. One can describe this extra uncertainty as loss of quantum coherence, or, equivalently, as uncertainty about the initial quantum state. The branching of little closed universes leadsto an infinite number of effective interactions. The strengths of these effective interactions cannot be predicted from the theory, but have to be fixed by measuring them. This implies that quantum gravity is effectively non-renormalizable, even if it is based on some finite underlying theory, such as superstrings.

Polycyclic aromatic hydrocarbons (PAH) occur widely in the lithosphere. They have been reported in various soils (Youngblood and Blumer, 1975; Laflamme and Hites, 1978), in marine sediments (Youngblood and Blumer, 1975; Hites et al, 1977), and in urban limnic sediments in the United States (Hites and Biemann, 1975; Wakeham, 1977) and in Europe (Grimmer and Bohnke, 1975; Muller et al, 1977; Giger and Schaffner, 1978). The concentrations of PAH range from less than 100 ppb for abyssal plain sediments to more than 100,000 ppb for sediments from highly urbanized areas. Much of the past work on the organic geochemistry of PAH has centered on understanding their sources, and there now seems to be a consesus (Youngblood and Blumer, 1975; Laflamme and Hites, 1978; Hites et al, 1977) that most (but not all) PAH in the sedimentary environment are due to combustion processes. However, little information is available on the mode(s) by which PAH are transported from the combustion source to the sediment. Existing data indicate high PAH levels at those locations which are close to centers of intense human activity and very low PAH levels at sites remote from anthropogenic influence. This is, however, only a qualitative observation which needs to be supplemented by a quantitative study. This paper represents such a study.

The Aharon-Vaidman (AV) game exemplifies the advantage of using simple quantum systems to outperform classical strategies. We present an experimental test of this quantum advantage by using a three-state quantum system (qutrit) encoded in a spatial mode of a single photon passing through a system of three slits. The preparation of a particular state is controlled as the photon propagates through the slits by varying the number of open slits and their respective phases. The measurements are achieved by placing detectors in the specific positions in the near and far-field after the slits. This set of tools allowed us to perform tomographic reconstructions of generalized qutrit states, and implement the quantum version of the AV game with compelling evidence of the quantum advantage.

Quantum fluctuations in the de Sitter phase of an inflationary Universe may produce the classical primordial density perturbations required to seed galaxies. Implicit in this theory is a prescription for extracting classical quantities from a quantum theory. We briefly review the original prescriptions for obtaining classical density perturbations. We then solve a simple toy model and show that the original prescriptions can be justified by applying decoherence arguments similar to those used in quantum cosmology.

We will present our recent results in the generation of triple photons as well as triple slits, both providing interesting perspectives on the foundations of quantum mechanics and quantum optics. The creation of correlated triple photons [1] is a highly desirable process for research on quantum optics, novel states of three-photon entanglement, and applications in quantum information processing. It was proposed over 20 years ago, but considered impossible to perform given the low conversion efficiencies in non-linear optics. We recently managed to solve the technical challenges, and demonstrate a source for correlated photon triplets. Strikingly, the interferences of single photons passing through a triple slit can be useful for experimental verification of Born's rule, which is at the heart of the formalism of quantum mechanics. We will illustrate the background of the argumentation, and show the elegant experimental setup, which allows this direct test of Born's rule[2].

The entropy of a Rindler wedge is calculated from the action of its complexified section using the method of Gibbons and Hawking. It is equal to one quarter the area of the event horizon in fundamental units.