21,161 research outputs found
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
Recommended from our members
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
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