568 research outputs found
Polynomial ergodicity and asymptotic behaviour of unbounded solutions of abstract evolution equations
In this paper we develop the notion of ergodicity to include functions
dominated by a weight . Such functions have polynomial means and include,
amongst many others, the -almost periodic functions. This enables us to
describe the asymptotic behaviour of unbounded solutions of linear evolution,
recurrence and convolution equations. To unify the treatment and allow for
further applications, we consider solutions of
generalized evolution equations of the form for where \ is a locally compact abelian group with a closed
subsemigroup , is a closed linear operator on a Banach space , is continuous and is a linear operator with characteristic
function . We introduce the resonance
set which contains the Beurling spectra of all
solutions of the homogeneous equation . For certain classes
{\F} of functions from to the spectrum sp_{{\F}}(\phi) of relative to is used to determine membership of {\F}. Our main
result gives general conditions under which sp_{{\F}}(\phi)\ is a subset of
the resonance set. As a simple consequence we obtain conditions under which
\psi |_{J}\in \F implies \phi |_{J}\in {\F}. An important tool is our
generalization to unbounded functions of a theorem of Loomis. As applications
we obtain generalizations or new proofs of many known results, including
theorems of Gelfand, Hille, Katznelson-Tzafriri, Esterle et al., Ph\'{o}ng,
Ruess and Arendt-Batty.Comment: 42 page
Violation of the Leggett-Garg inequality with weak measurements of photons
By weakly measuring the polarization of a photon between two strong
polarization measurements, we experimentally investigate the correlation
between the appearance of anomalous values in quantum weak measurements, and
the violation of realism and non-intrusiveness of measurements. A quantitative
formulation of the latter concept is expressed in terms of a Leggett-Garg
inequality for the outcomes of subsequent measurements of an individual quantum
system. We experimentally violate the Leggett-Garg inequality for several
measurement strengths. Furthermore, we experimentally demonstrate that there is
a one-to-one correlation between achieving strange weak values and violating
the Leggett-Garg inequality.Comment: 5 pages, 4 figure
Creation of Maximally Entangled Photon Number States using Optical Fibre Multiports
We theoretically demonstrate a method for producing the maximally path-entangled state (1/Sqrt[2]) (|N,0> + exp[iN phi] |0,N>) using intensity-symmetric multiport beamsplitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state
Time-reversal and super-resolving phase measurements
We demonstrate phase super-resolution in the absence of entangled states. The
key insight is to use the inherent time-reversal symmetry of quantum mechanics:
our theory shows that it is possible to \emph{measure}, as opposed to prepare,
entangled states. Our approach is robust, requiring only photons that exhibit
classical interference: we experimentally demonstrate high-visibility phase
super-resolution with three, four, and six photons using a standard laser and
photon counters. Our six-photon experiment demonstrates the best phase
super-resolution yet reported with high visibility and resolution.Comment: 4 pages, 3 figure
High-Fidelity Z-Measurement Error Correction of Optical Qubits
We demonstrate a quantum error correction scheme that protects against
accidental measurement, using an encoding where the logical state of a single
qubit is encoded into two physical qubits using a non-deterministic photonic
CNOT gate. For the single qubit input states |0>, |1>, |0>+|1>, |0>-|1>,
|0>+i|1>, and |0>-i|1> our encoder produces the appropriate 2-qubit encoded
state with an average fidelity of 0.88(3) and the single qubit decoded states
have an average fidelity of 0.93(5) with the original state. We are able to
decode the 2-qubit state (up to a bit flip) by performing a measurement on one
of the qubits in the logical basis; we find that the 64 1-qubit decoded states
arising from 16 real and imaginary single qubit superposition inputs have an
average fidelity of 0.96(3).Comment: 4 pages, 4 figures, comments welcom
Elements of rings with equal spectral idempotents
In this paper we define and study a generalized Drazin inverse for ring elements , and
give a characterization of elements for which .
We apply our results to the study of EP elements of a ring with involution.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI)
Quantum gate characterization in an extended Hilbert space
We describe an approach for characterizing the process of quantum gates using
quantum process tomography, by first modeling them in an extended Hilbert
space, which includes non-qubit degrees of freedom. To prevent unphysical
processes from being predicted, present quantum process tomography procedures
incorporate mathematical constraints, which make no assumptions as to the
actual physical nature of the system being described. By contrast, the
procedure presented here ensures physicality by placing physical constraints on
the nature of quantum processes. This allows quantum process tomography to be
performed using a smaller experimental data set, and produces parameters with a
direct physical interpretation. The approach is demonstrated by example of
mode-matching in an all-optical controlled-NOT gate. The techniques described
are non-specific and could be applied to other optical circuits or quantum
computing architectures.Comment: 4 pages, 2 figures, REVTeX (published version
Demonstration of a simple entangling optical gate and its use in Bell-state analysis
We demonstrate a new architecture for an optical entangling gate that is
significantly simpler than previous realisations, using partially-polarising
beamsplitters so that only a single optical mode-matching condition is
required. We demonstrate operation of a controlled-Z gate in both
continuous-wave and pulsed regimes of operation, fully characterising it in
each case using quantum process tomography. We also demonstrate a
fully-resolving, nondeterministic optical Bell-state analyser based on this
controlled-Z gate. This new architecture is ideally suited to guided optics
implementations of optical gates.Comment: 4 pages, 3 figures. v2: additional author, improved data and figures
(low res), some other minor changes. Accepted for publication in PR
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