8,803 research outputs found
Quantum Fidelity Decay of Quasi-Integrable Systems
We show, via numerical simulations, that the fidelity decay behavior of
quasi-integrable systems is strongly dependent on the location of the initial
coherent state with respect to the underlying classical phase space. In
parallel to classical fidelity, the quantum fidelity generally exhibits
Gaussian decay when the perturbation affects the frequency of periodic phase
space orbits and power-law decay when the perturbation changes the shape of the
orbits. For both behaviors the decay rate also depends on initial state
location. The spectrum of the initial states in the eigenbasis of the system
reflects the different fidelity decay behaviors. In addition, states with
initial Gaussian decay exhibit a stage of exponential decay for strong
perturbations. This elicits a surprising phenomenon: a strong perturbation can
induce a higher fidelity than a weak perturbation of the same type.Comment: 11 pages, 11 figures, to be published Phys. Rev.
Quantum Sensor Miniaturization
The classical bound on image resolution defined by the Rayleigh limit can be
beaten by exploiting the properties of quantum mechanical entanglement. If
entangled photons are used as signal states, the best possible resolution is
instead given by the Heisenberg limit, an improvement proportional to the
number of entangled photons in the signal. In this paper we present a novel
application of entanglement by showing that the resolution obtained by an
imaging system utilizing separable photons can be achieved by an imaging system
making use of entangled photons, but with the advantage of a smaller aperture,
thus resulting in a smaller and lighter system. This can be especially valuable
in satellite imaging where weight and size play a vital role.Comment: 3 pages, 1 figure. Accepted for publication in Photonics Technology
Letter
Implementation of the Quantum Fourier Transform
The quantum Fourier transform (QFT) has been implemented on a three bit
nuclear magnetic resonance (NMR) quantum computer, providing a first step
towards the realization of Shor's factoring and other quantum algorithms.
Implementation of the QFT is presented with fidelity measures, and state
tomography. Experimentally realizing the QFT is a clear demonstration of NMR's
ability to control quantum systems.Comment: 6 pages, 2 figure
Fidelity Decay as an Efficient Indicator of Quantum Chaos
Recent work has connected the type of fidelity decay in perturbed quantum
models to the presence of chaos in the associated classical models. We
demonstrate that a system's rate of fidelity decay under repeated perturbations
may be measured efficiently on a quantum information processor, and analyze the
conditions under which this indicator is a reliable probe of quantum chaos and
related statistical properties of the unperturbed system. The type and rate of
the decay are not dependent on the eigenvalue statistics of the unperturbed
system, but depend on the system's eigenvector statistics in the eigenbasis of
the perturbation operator. For random eigenvector statistics the decay is
exponential with a rate fixed precisely by the variance of the perturbation's
energy spectrum. Hence, even classically regular models can exhibit an
exponential fidelity decay under generic quantum perturbations. These results
clarify which perturbations can distinguish classically regular and chaotic
quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction
and discussion
I=3/2 Scattering in the Nonrelativisitic Quark Potential Model
We study elastic scattering to Born order using
nonrelativistic quark wavefunctions in a constituent-exchange model. This
channel is ideal for the study of nonresonant meson-meson scattering amplitudes
since s-channel resonances do not contribute significantly. Standard quark
model parameters yield good agreement with the measured S- and P-wave phase
shifts and with PCAC calculations of the scattering length. The P-wave phase
shift is especially interesting because it is nonzero solely due to
symmetry breaking effects, and is found to be in good agreement with experiment
given conventional values for the strange and nonstrange constituent quark
masses.Comment: 12 pages + 2 postscript figures, Revtex, MIT-CTP-210
On the geometric quantization of twisted Poisson manifolds
We study the geometric quantization process for twisted Poisson manifolds.
First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for
twisted Poisson manifolds and we use it in order to characterize their
prequantization bundles and to establish their prequantization condition. Next,
we introduce a polarization and we discuss the quantization problem. In each
step, several examples are presented
Modular classes of Poisson-Nijenhuis Lie algebroids
The modular vector field of a Poisson-Nijenhuis Lie algebroid is defined
and we prove that, in case of non-degeneracy, this vector field defines a
hierarchy of bi-Hamiltonian -vector fields. This hierarchy covers an
integrable hierarchy on the base manifold, which may not have a
Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic
Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
Control over electron-spin states, such as coherent manipulation, filtering
and measurement promises access to new technologies in conventional as well as
in quantum computation and quantum communication. We review our proposal of
using electron spins in quantum confined structures as qubits and discuss the
requirements for implementing a quantum computer. We describe several
realizations of one- and two-qubit gates and of the read-in and read-out tasks.
We discuss recently proposed schemes for using a single quantum dot as
spin-filter and spin-memory device. Considering electronic EPR pairs needed for
quantum communication we show that their spin entanglement can be detected in
mesoscopic transport measurements using metallic as well as superconducting
leads attached to the dots.Comment: Prepared for Fortschritte der Physik special issue, Experimental
Proposals for Quantum Computation. 15 pages, 5 figures; typos corrected,
references adde
Modular classes of skew algebroid relations
Skew algebroid is a natural generalization of the concept of Lie algebroid.
In this paper, for a skew algebroid E, its modular class mod(E) is defined in
the classical as well as in the supergeometric formulation. It is proved that
there is a homogeneous nowhere-vanishing 1-density on E* which is invariant
with respect to all Hamiltonian vector fields if and only if E is modular, i.e.
mod(E)=0. Further, relative modular class of a subalgebroid is introduced and
studied together with its application to holonomy, as well as modular class of
a skew algebroid relation. These notions provide, in particular, a unified
approach to the concepts of a modular class of a Lie algebroid morphism and
that of a Poisson map.Comment: 20 page
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