Single-Step Distillation Protocol with Generalized Beam Splitters

We develop a distillation protocol for multilevel qubits (qudits) using generalized beam splitters like in the proposal of Pan et al. for ordinary qubits. We find an acceleration with respect to the scheme of Bennet et al. when extended to qudits. It is also possible to distill entangled pairs of photons carrying orbital angular momenta (OAM) states that conserves the total angular momenta as those produced in recent experiments.Comment: REVTEX4 file, color figure

Distillation Protocols for Mixed States of Multilevel Qubits and the Quantum Renormalization Group

We study several properties of distillation protocols to purify multilevel qubit states (qudits) when applied to a certain family of initial mixed bipartite states. We find that it is possible to use qudits states to increase the stability region obtained with the flow equations to distill qubits. In particular, for qutrits we get the phase diagram of the distillation process with a rich structure of fixed points. We investigate the large-$D$ limit of qudits protocols and find an analytical solution in the continuum limit. The general solution of the distillation recursion relations is presented in an appendix. We stress the notion of weight amplification for distillation protocols as opposed to the quantum amplitude amplification that appears in the Grover algorithm. Likewise, we investigate the relations between quantum distillation and quantum renormalization processes.Comment: REVTEX4 file, 12 pages, 3 tables, color figure

A paradox in bosonic energy computations via semidefinite programming relaxations

We show that the recent hierarchy of semidefinite programming relaxations based on non-commutative polynomial optimization and reduced density matrix variational methods exhibits an interesting paradox when applied to the bosonic case: even though it can be rigorously proven that the hierarchy collapses after the first step, numerical implementations of higher order steps generate a sequence of improving lower bounds that converges to the optimal solution. We analyze this effect and compare it with similar behavior observed in implementations of semidefinite programming relaxations for commutative polynomial minimization. We conclude that the method converges due to the rounding errors occurring during the execution of the numerical program, and show that convergence is lost as soon as computer precision is incremented. We support this conclusion by proving that for any element p of a Weyl algebra which is non-negative in the Schrodinger representation there exists another element p' arbitrarily close to p that admits a sum of squares decomposition.Comment: 22 pages, 4 figure

Cool stars in NGC 2547 and pre main sequence lithium depletion

We present the results of a spectroscopic survey of X-ray selected, low-mass candidate members of the young open cluster NGC 2547. Using a combination of photometry, spectroscopic indices and radial velocities we refine our candidate list and then use our spectroscopy to study the progression of lithium depletion in low-mass pre main sequence stars. We derive lithium abundances or upper limits for all our candidate members, which have effective temperatures in the range 5000>Teff>3200K, and compare these with predictions for lithium burning and depletion provided by a number of models and also with the lithium depletion seen in younger and older stars. We find that some models can reproduce the lithium abundance pattern of NGC 2547 if the cluster has an age of ~20-35Myr, which is also indicated by fits to low-mass isochrones in the Hertzsprung-Russell diagram. But the lack of significant further lithium depletion between NGC 2547 and older clusters argues for an age of at least 50Myr, more in keeping with the lack of lithium observed in even fainter NGC 2547 candidates. We show that reconciliation of these age estimates may require additions to the physics incorporated in current generations of pre main sequence models.Comment: Accepted for publication in MNRAS (better version of Fig.1 available at http://www.astro.keele.ac.uk/~rdj/

Experimental Proof of Quantum Nonlocality without Squeezing

It is shown that the ensemble $\{p (\alpha),|\alpha>|\alpha^*>\}$ where $p (\alpha)$ is a Gaussian distribution of finite variance and $| \alpha>$ is a coherent state can be better discriminated with an entangled measurement than with any local strategy supplemented by classical communication. Although this ensemble consists of products of quasi-classical states, it exhibits some quantum nonlocality. This remarkable effect is demonstrated experimentally by implementing the optimal local strategy together with a joint nonlocal strategy that yields a higher fidelity.Comment: 4 pages, 2 figure