The breeding of sugarcane

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Unforgeable Noise-Tolerant Quantum Tokens

The realization of devices which harness the laws of quantum mechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of "quantum money". A dishonest holder of a quantum bank-note will invariably fail in any forging attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence and operational imperfections abound. Thus, the development of secure "quantum money"-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store and measure single qubit quantum memories, making their experimental realization accessible with current technologies.Comment: 18 pages, 5 figure

New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

Optimal approach to quantum communication using dynamic programming

Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished via noisy channels (such as optical fibers) that generally result in exponential attenuation of quantum signals at large distances. A special class of quantum error correction protocols--quantum repeater protocols--can be used to overcome such losses. In this work, we introduce a method for systematically optimizing existing protocols and developing new, more efficient protocols. Our approach makes use of a dynamic programming-based searching algorithm, the complexity of which scales only polynomially with the communication distance, letting us efficiently determine near-optimal solutions. We find significant improvements in both the speed and the final state fidelity for preparing long distance entangled states.Comment: 9 pages, 6 figure

Semiclassical wave equation and exactness of the WKB method

The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB quantization condition to this equation reproduces exact energy eigenvalues for all solvable spherically symmetric potentials.Comment: 13 page

Renormalization--Group Solutions for Yukawa Potential

The self--similar renormalization group is used to obtain expressions for the spectrum of the Hamiltonian with the Yukawa potential. The critical screening parameter above which there are no bound states is also obtained by this method. The approach presented illustrates that one can achieve good accuracy without involving extensive numerical calculations, but invoking instead the renormalization--group techniques.Comment: 1 file, 12 pages, RevTe

A note on the breeding of sugarcane varieties resistant to mosaic

The behaviour of certain Coimbatore sugarcane varieties with reference to the mosaic disease has been discussed, showing that those containingSaccharum spontaneum blood are generally resistant or at least tolerant. Preliminary data regarding the supposed correlation between bristles and mosaic resistance have been presented, which indicate that at least in certain cases there appears to be no positive correlation between the high number of bristles and disease resistance, nor in the protection supposed to be afforded by the bristles to the stomata