Optimal multicopy asymmetric Gaussian cloning of coherent states

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas, such that the fidelity of all copies may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines.Comment: 7 pages, 2 figures, RevTeX

A lower bound on the two-arms exponent for critical percolation on the lattice

We consider the standard site percolation model on the $d$-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505-531] is that the two-arms exponent is larger than or equal to $1/2$. We improve slightly this lower bound in any dimension $d\geq2$. Next, starting only with the hypothesis that $\theta(p)>0$, without using the slab technology, we derive a quantitative estimate establishing long-range order in a finite box.Comment: Published at http://dx.doi.org/10.1214/14-AOP940 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cloning a Qutrit

We investigate several classes of state-dependent quantum cloners for three-level systems. These cloners optimally duplicate some of the four maximally-conjugate bases with an equal fidelity, thereby extending the phase-covariant qubit cloner to qutrits. Three distinct classes of qutrit cloners can be distinguished, depending on two, three, or four maximally-conjugate bases are cloned as well (the latter case simply corresponds to the universal qutrit cloner). These results apply to symmetric as well as asymmetric cloners, so that the balance between the fidelity of the two clones can also be analyzed.Comment: 14 pages LaTex. To appear in the Journal of Modern Optics for the special issue on "Quantum Information: Theory, Experiment and Perspectives". Proceedings of the ESF Conference, Gdansk, July 10-18, 200

Nullification Writhe and Chirality of Alternating Links

In this paper, we show how to split the writhe of reduced projections of oriented alternating links into two parts, called nullification writhe, or wx, and remaining writhe, or wy, such that the sum of these quantities equals the writhe w, and each quantity remains an invariant of isotopy. The chirality of oriented alternating links can be detected by a non-zero wx or wy, which constitutes an improvement compared to the detection of chirality by a non-zero w. An interesting corollary is that all oriented alternating links with an even number of components are chiral, a result that also follows from properties of the Conway polynomial.Comment: AMS-LaTeX, 12 pages with 14 figure