2,446 research outputs found
Matrix Element Distribution as a Signature of Entanglement Generation
We explore connections between an operator's matrix element distribution and
its entanglement generation. Operators with matrix element distributions
similar to those of random matrices generate states of high multi-partite
entanglement. This occurs even when other statistical properties of the
operators do not conincide with random matrices. Similarly, operators with some
statistical properties of random matrices may not exhibit random matrix element
distributions and will not produce states with high levels of multi-partite
entanglement. Finally, we show that operators with similar matrix element
distributions generate similar amounts of entanglement.Comment: 7 pages, 6 figures, to be published PRA, partially supersedes
quant-ph/0405053, expands quant-ph/050211
Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution
We study the interrelations between the classical (Frobenius-Perron) and the
quantum (Husimi) propagator for phase-space (quasi-)probability densities in a
Hamiltonian system displaying a mix of regular and chaotic behavior. We focus
on common resonances of these operators which we determine by blurring
phase-space resolution. We demonstrate that classical and quantum time
evolution look alike if observed with a resolution much coarser than a Planck
cell and explain how this similarity arises for the propagators as well as
their spectra. The indistinguishability of blurred quantum and classical
evolution implies that classical resonances can conveniently be determined from
quantum mechanics and in turn become effective for decay rates of quantum
correlations.Comment: 10 pages, 3 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
Overdamping by weakly coupled environments
A quantum system weakly interacting with a fast environment usually undergoes
a relaxation with complex frequencies whose imaginary parts are damping rates
quadratic in the coupling to the environment, in accord with Fermi's ``Golden
Rule''. We show for various models (spin damped by harmonic-oscillator or
random-matrix baths, quantum diffusion, quantum Brownian motion) that upon
increasing the coupling up to a critical value still small enough to allow for
weak-coupling Markovian master equations, a new relaxation regime can occur. In
that regime, complex frequencies lose their real parts such that the process
becomes overdamped. Our results call into question the standard belief that
overdamping is exclusively a strong coupling feature.Comment: 4 figures; Paper submitted to Phys. Rev.
Field quantization for chaotic resonators with overlapping modes
Feshbach's projector technique is employed to quantize the electromagnetic
field in optical resonators with an arbitray number of escape channels. We find
spectrally overlapping resonator modes coupled due to the damping and noise
inflicted by the external radiation field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.Comment: 4 pages, 1 figur
Characterization of complex quantum dynamics with a scalable NMR information processor
We present experimental results on the measurement of fidelity decay under
contrasting system dynamics using a nuclear magnetic resonance quantum
information processor. The measurements were performed by implementing a
scalable circuit in the model of deterministic quantum computation with only
one quantum bit. The results show measurable differences between regular and
complex behaviour and for complex dynamics are faithful to the expected
theoretical decay rate. Moreover, we illustrate how the experimental method can
be seen as an efficient way for either extracting coarse-grained information
about the dynamics of a large system, or measuring the decoherence rate from
engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that
publishe
Finite-difference distributions for the Ginibre ensemble
The Ginibre ensemble of complex random matrices is studied. The complex
valued random variable of second difference of complex energy levels is
defined. For the N=3 dimensional ensemble are calculated distributions of
second difference, of real and imaginary parts of second difference, as well as
of its radius and of its argument (angle). For the generic N-dimensional
Ginibre ensemble an exact analytical formula for second difference's
distribution is derived. The comparison with real valued random variable of
second difference of adjacent real valued energy levels for Gaussian
orthogonal, unitary, and symplectic, ensemble of random matrices as well as for
Poisson ensemble is provided.Comment: 8 pages, a number of small changes in the tex
The Effects of Symmetries on Quantum Fidelity Decay
We explore the effect of a system's symmetries on fidelity decay behavior.
Chaos-like exponential fidelity decay behavior occurs in non-chaotic systems
when the system possesses symmetries and the applied perturbation is not tied
to a classical parameter. Similar systems without symmetries exhibit
faster-than-exponential decay under the same type of perturbation. This
counter-intuitive result, that extra symmetries cause the system to behave in a
chaotic fashion, may have important ramifications for quantum error correction.Comment: 5 pages, 3 figures, to be published Phys. Rev. E Rapid Communicatio
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