Natural three-qubit interactions in one-way quantum computing

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation (\QC). A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.Comment: 4 pages, 3 figures, RevTeX

Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its ``purification''. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein-Gordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its ``purification'' induces on the one-particle space of the quantized system a topology which coincides with that given by the two-point functions of quasifree Hadamard states. These findings will be shown to lead to new results concerning the structure of the local (von Neumann) observable-algebras in representations of quasifree Hadamard states of the Klein-Gordon field in an arbitrary globally hyperbolic spacetime, such as local definiteness, local primarity and Haag-duality (and also split- and type III_1-properties). A brief review of this circle of notions, as well as of properties of Hadamard states, forms part of the article.Comment: 42 pages, LaTeX. The Def. 3.3 was incomplete and this has been corrected. Several misprints have been removed. All results and proofs remain unchange

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain `base points' of the Cauchy horizon, which are defined as `past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's `Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a `time machine'. Specifically, we prove: Theorem 1: There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2: The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in MXM) of (x,x). Theorem 2 implies quantities such as the renormalized expectation value of \phi^2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proofs rely on the `Propagation of Singularities' theorems of Duistermaat and H\"ormander.Comment: 37 pages, LaTeX, uses latexsym and amsbsy, no figures; updated version now published in Commun. Math. Phys.; no major revisions from original versio

Limits of sensing temporal concentration changes by single cells

Berg and Purcell [Biophys. J. 20, 193 (1977)] calculated how the accuracy of concentration sensing by single-celled organisms is limited by noise from the small number of counted molecules. Here we generalize their results to the sensing of concentration ramps, which is often the biologically relevant situation (e.g. during bacterial chemotaxis). We calculate lower bounds on the uncertainty of ramp sensing by three measurement devices: a single receptor, an absorbing sphere, and a monitoring sphere. We contrast two strategies, simple linear regression of the input signal versus maximum likelihood estimation, and show that the latter can be twice as accurate as the former. Finally, we consider biological implementations of these two strategies, and identify possible signatures that maximum likelihood estimation is implemented by real biological systems.Comment: 11 pages, 2 figure

Fisher-information condition for enhanced signal detection via stochastic resonance

Various situations where a signal is enhanced by noise through stochastic resonance are now known. This paper contributes to determining general conditions under which improvement by noise can be a priori decided as feasible or not. We focus on the detection of a known signal in additive white noise. Under the assumptions of a weak signal and a sufficiently large sample size, it is proved, with an inequality based on the Fisher information, that improvement by adding noise is never possible, generically, in these conditions. However, under less restrictive conditions, an example of signal detection is shown with favorable action of adding noise.Fabing Duan, François Chapeau-Blondeau, Derek Abbot

Generating quantum states through spin chain dynamics

Spin chains can realise perfect quantum state transfer between the two ends via judicious choice of coupling strengths. In this paper, we study what other states can be created by engineering a spin chain. We conclude that, up to local phases, all single excitation quantum states with support on every site of the chain can be created. We pay particular attention to the generation of W-states that are superposed over every site of the chain.Comment: 9 pages, 1 figur

Entanglement generation in harmonic chains: tagging by squeezing

We address the problem of spring-like coupling between bosons in an open chain configuration where the counter-rotating terms are explicitly included. We show that fruitful insight can be gained by decomposing the time-evolution operator of this problem into a pattern of linear-optics elements. This allows us to provide a clear picture of the effects of the counter-rotating terms in the important problem of long-haul entanglement distribution. The analytic control over the variance matrix of the state of the bosonic register allows us to track the dynamics of the entanglement. This helps in designing a global addressing scheme, complemented by a proper initialization of the register, which quantitatively improves the entanglement between the extremal oscillators in the chain, thus providing a strategy for feasible long distance entanglement distribution.Comment: 8 pages, 8 figures, RevTeX

The thermal and two-particle stress-energy must be ill-defined on the 2-d Misner space chronology horizon

We show that an analogue of the (four dimensional) image sum method can be used to reproduce the results, due to Krasnikov, that for the model of a real massless scalar field on the initial globally hyperbolic region IGH of two-dimensional Misner space there exist two-particle and thermal Hadamard states (built on the conformal vacuum) such that the (expectation value of the renormalised) stress-energy tensor in these states vanishes on IGH. However, we shall prove that the conclusions of a general theorem by Kay, Radzikowski and Wald still apply for these states. That is, in any of these states, for any point b on the Cauchy horizon and any neighbourhood N of b, there exists at least one pair of non-null related points (x,x'), with x and x' in the intersection of IGH with N, such that (a suitably differentiated form of) its two-point function is singular. (We prove this by showing that the two-point functions of these states share the same singularities as the conformal vacuum on which they are built.) In other words, the stress-energy tensor in any of these states is necessarily ill-defined on the Cauchy horizon.Comment: 6 pages, LaTeX, RevTeX, no figure

Developing professionalism in new IT graduates? Who needs it?

A new graduate may require a period of ‘acclimatisation’ through a process of ‘developing their professionalism’ to fit into their work environment. The e-Skills UK Technology Counts Insights 2010 report suggests that 110,500 new entrants a year are required to fill IT & Telecoms professional job roles, with 20,800 coming from education (predominantly graduate level and higher). However, 43% of recruiters were reporting a lack of suitable candidates for IT & Telecoms posts where growing importance will be placed on relationship management, business process analysis and design, project and programme management. IT & Telecoms professionals are increasingly expected to be multi-skilled, with sophisticated business and interpersonal skills as well as technical competence. As the report also says: ‘UK growth will continue to be primarily in high-value roles with an increasing need for customer and business-oriented skills as well as sophisticated technical competencies.’ The diverse needs and requirements of the IT sector, as specified by various employer groups and professional bodies including BCS, IET, eSkills, the CBI and the SFIA Foundation, are discussed. According to the CBI, ‘62% of entrants to the IT sector need to draw on managerial and professional business skills almost immediately.’ For organisations to succeed, their IT graduate recruits must supplement their IT skills with managerial and professional business skills. Well considered CPD will ensure that recent graduates can enhance their ‘academic’ skills with the necessary work-based skills for the benefit of both themselves and their new employer. The focus of the improvement will balance the student-centred needs for development and the engaging employer’s commercial needs

Quantum Communication in Spin Systems With Long-Range Interactions

We calculate the fidelity of transmission of a single qubit between distant sites on semi-infinite and finite chains of spins coupled via the magnetic dipole interaction. We show that such systems often perform better than their Heisenberg nearest-neighbour coupled counterparts, and that fidelities closely approaching unity can be attained between the ends of finite chains without any special engineering of the system, although state transfer becomes slow in long chains. We discuss possible optimization methods, and find that, for any length, the best compromise between the quality and the speed of the communication is obtained in a nearly uniform chain of 4 spins.Comment: 15 pages, 8 eps figures, updated references, corrected text and corrected figs. 1, 4 and