High-efficiency cluster-state generation with atomic ensembles via the dipole-blockade mechanism

We demonstrate theoretically a scheme for cluster-state generation, based on atomic ensembles and the dipole-blockade mechanism. In the protocol, atomic ensembles serve as single-qubit systems. Therefore, we review single-qubit operations on qubit defined as collective states of atomic ensemble. Our entangling protocol requires nearly identical single-photon sources, one ultracold ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates in a single step Q-qubit GHZ states with success probability p(success) similar to eta(Q/2), where eta is the combined detection and source efficiency. This is significantly more efficient than any known robust probabilistic entangling operation. GHZ states form the basic building block for universal cluster states, a resource for the one-way quantum computer

Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates

The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the Cramer-Rao bound.Comment: 22 pages, 4 figure

Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information

A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/ where G is the generator of the shift (with an arbitrary discrete or continuous spectrum), and hence establishes a universally applicable bound of the same form as the usual Heisenberg limit. The scaling constant k_I depends on prior information about the shift parameter. For example, in phase sensing regimes, where the phase shift is confined to some small interval of length L, the relative resolution \delta\hat{\Phi}/L has the strict lower bound (2\pi e^3)^{-1/2}/, where m is the number of probes, each with generator G_1, and entangling joint measurements are permitted. Generalisations using other resource measures and including noise are briefly discussed. The results rely on the derivation of general entropic uncertainty relations for continuous observables, which are of interest in their own right.Comment: v2:new bound added for 'ignorance respecting estimates', some clarification

Gaussian quantum computation with oracle-decision problems

We study a simple-harmonic-oscillator quantum computer solving oracle decision problems. We show that such computers can perform better by using nonorthogonal Gaussian wave functions rather than orthogonal top-hat wave functions as input to the information encoding process. Using the Deutsch-Jozsa problem as an example, we demonstrate that Gaussian modulation with optimized width parameter results in a lower error rate than for the top-hat encoding. We conclude that Gaussian modulation can allow for an improved trade-off between encoding, processing and measurement of the information.Comment: RevTeX4, 10 pages with 4 figure

On arbitrages arising from honest times

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.Comment: 25 pages, revised versio

Complex exon-intron marking by histone modifications is not determined solely by nucleosome distribution

It has recently been shown that nucleosome distribution, histone modifications and RNA polymerase II (Pol II) occupancy show preferential association with exons (“exon-intron marking”), linking chromatin structure and function to co-transcriptional splicing in a variety of eukaryotes. Previous ChIP-sequencing studies suggested that these marking patterns reflect the nucleosomal landscape. By analyzing ChIP-chip datasets across the human genome in three cell types, we have found that this marking system is far more complex than previously observed. We show here that a range of histone modifications and Pol II are preferentially associated with exons. However, there is noticeable cell-type specificity in the degree of exon marking by histone modifications and, surprisingly, this is also reflected in some histone modifications patterns showing biases towards introns. Exon-intron marking is laid down in the absence of transcription on silent genes, with some marking biases changing or becoming reversed for genes expressed at different levels. Furthermore, the relationship of this marking system with splicing is not simple, with only some histone modifications reflecting exon usage/inclusion, while others mirror patterns of exon exclusion. By examining nucleosomal distributions in all three cell types, we demonstrate that these histone modification patterns cannot solely be accounted for by differences in nucleosome levels between exons and introns. In addition, because of inherent differences between ChIP-chip array and ChIP-sequencing approaches, these platforms report different nucleosome distribution patterns across the human genome. Our findings confound existing views and point to active cellular mechanisms which dynamically regulate histone modification levels and account for exon-intron marking. We believe that these histone modification patterns provide links between chromatin accessibility, Pol II movement and co-transcriptional splicing