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

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

Cloning quantum entanglement in arbitrary dimensions

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of all isotropic states. For large $d$, the entanglement of formation of each clone tends to one half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one fourth the input entanglement in the large-$d$ limit.Comment: 6 pages, 3 figure

Cloning a real d-dimensional quantum state on the edge of the no-signaling condition

We investigate a new class of quantum cloning machines that equally duplicate all real states in a Hilbert space of arbitrary dimension. By using the no-signaling condition, namely that cloning cannot make superluminal communication possible, we derive an upper bound on the fidelity of this class of quantum cloning machines. Then, for each dimension d, we construct an optimal symmetric cloner whose fidelity saturates this bound. Similar calculations can also be performed in order to recover the fidelity of the optimal universal cloner in d dimensions.Comment: 6 pages RevTex, 1 encapuslated Postscript figur

Monte Carlo computation of pair correlations in excited nuclei

We present a novel quantum Monte Carlo method based on a path integral in Fock space, which allows to compute finite-temperature properties of a many-body nuclear system with a monopole pairing interaction in the canonical ensemble. It enables an exact calculation of the thermodynamic variables such as the internal energy, the entropy, or the specific heat, from the measured moments of the number of hops in a path of nuclear configurations. Monte Carlo calculations for a single-shell $(h_{11/2})^6$ model are consistent with an exact calculation from the many-body spectrum in the seniority model.Comment: 5 pages uuencoded Postscrip

A No-Go Theorem for Gaussian Quantum Error Correction

It is proven that Gaussian operations are of no use for protecting Gaussian states against Gaussian errors in quantum communication protocols. Specifically, we introduce a new quantity characterizing any single-mode Gaussian channel, called entanglement degradation, and show that it cannot decrease via Gaussian encoding and decoding operations only. The strength of this no-go theorem is illustrated with some examples of Gaussian channels.Comment: 4 pages, 2 figures, REVTeX