Classical Homomorphic Encryption for Quantum Circuits

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem

Classical Verification of Quantum Computations

We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum prover as a trusted measurement device. The protocol forces the prover to behave as follows: the prover must construct an n qubit state of his choice, measure each qubit in the Hadamard or standard basis as directed by the verifier, and report the measurement results to the verifier. The soundness of this protocol is enforced based on the assumption that the learning with errors problem is computationally intractable for efficient quantum machines

Introduction: Religious plurality, interreligious pluralism, and spatialities of religious difference

The introduction to this special section foregrounds the key distinction between ‘religious plurality’ and ‘interreligious pluralism’. Building from the example of a recent controversy over an exhibition on shared religious sites in Thessaloniki, Greece, we analyze the ways in which advocates and adversaries of pluralism alternately place minority religions at the center or attempt to relegate them to the margins of visual, spatial, and political fields. To establish the conceptual scaffolding that supports this special section, we engage the complex relations that govern the operations of state and civil society, sacrality and secularity, as well as spectacular acts of disavowal that simultaneously coincide with everyday multiplicities in the shared use of space. We conclude with brief summaries of the four articles that site religious plurality and interreligious pluralism in the diverse contexts of Brazil, Russia, Sri Lanka, and the Balkans

Rational approximations and quantum algorithms with postselection

We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We give optimal (up to constant factors) quantum algorithms with postselection for the Majority function, slightly improving upon an earlier algorithm of Aaronson. Finally we show how Newman's classic theorem about low-degree rational approximation of the absolute-value function follows from these algorithms.Comment: v2: 12 pages LaTeX, to appear in Quantum Information and Computation. Compared to version 1, the writing has been improved but the results are unchange

Axially symmetric, asymptotically flat vacuum metric with a naked singularity and closed timelike curves

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature singularity. The spacetime is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the spacetime also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.Comment: 8 pages, no figure

Right-handed Majorana Neutrino Mass Matrices for Generating Bimaximal Mixings in Degenerate and Inverted Models of Neutrinos

An attempt is made to generate the bimaximal mixings of the three species of neutrinos from the textures of the right-handed Majorana neutrino mass matrices. We extend our earlier work in this paper for the generation of the nearly degenerate as well as the inverted hierarchical models of the left-handed Majorana neutrino mass matrices using the non-diagonal textures of the right-handed Majorana neutrino mass matrices and the diagonal form of the Dirac neutrino mass matrices, within the frame work of the seesaw mechanism in a model independent way. Such Majorana neutrino mass models are important to explain the recently reported result on the neutrinoless double beat decay (0/nu/beta/beta) experiment,together with the earlier established data on LMA MSW solar and atmospheric neutrino oscillations.Comment: 14 pages, To appear in IJMPA (2003

Climate Effects on Black Spruce and Trembling Aspen Productivity in Natural Origin Mixed Stands

Forest managers need site productivity estimates for tree species growing in mixed stands. Models developed in the past are generally for pure stands and don’t factor in the effects of climate change on site productivity. Therefore, site index (SI) models were developed for black spruce (Picea mariana Mill. B.S.P.) and trembling aspen (Populus tremuloides Michx.) trees grown in natural origin mixed stands. For this, 186 trees (93 black spruce and trembling aspen each) were sampled from 31 even-aged natural mixed stands (sites) (3 trees/species/site) across Ontario, Canada. Stand height growth models were developed by incorporating climate variables during growth for each species. Stem analysis data collected from sampled trees were used to develop these models. A mixed effects modelling approach was used to fit the models. The relationship between SIs of black spruce and trembling aspen grown in mixed stands was analyzed by calculating correlation coefficients and plotting black spruce SIs against those of trembling aspen. Climate effects on site productivity were evaluated by predicting stand heights for 4 geographic areas of Ontario for the period 2021 to 2080. Three emissions scenarios reflecting different amounts of heat at the end of the century (i.e., 2.6, 4.5, and 8.5 watts m-2 ) were used in the stand height growth models developed here for evaluation. Climate effects were more pronounced for trembling aspen than black spruce only in the far west. The relationship between SIs of black spruce and trembling aspen trees grown in natural origin mixed stands could not be described using a linear/nonlinear mathematical function. The models developed here can be used to estimate stand height and SI of black spruce and trembling aspen trees grown in natural origin mixed stands in a changing climate. In the absence of climate data, models fitted without climate variables can be used to estimate SI of both species