4,073 research outputs found
Entangling power of the quantum baker's map
We investigate entanglement production in a class of quantum baker's maps.
The dynamics of these maps is constructed using strings of qubits, providing a
natural tensor-product structure for application of various entanglement
measures. We find that, in general, the quantum baker's maps are good at
generating entanglement, producing multipartite entanglement amongst the qubits
close to that expected in random states. We investigate the evolution of
several entanglement measures: the subsystem linear entropy, the concurrence to
characterize entanglement between pairs of qubits, and two proposals for a
measure of multipartite entanglement. Also derived are some new analytical
formulae describing the levels of entanglement expected in random pure states.Comment: 22 pages, 11 figure
Generalized uncertainty relations: Theory, examples, and Lorentz invariance
The quantum-mechanical framework in which observables are associated with
Hermitian operators is too narrow to discuss measurements of such important
physical quantities as elapsed time or harmonic-oscillator phase. We introduce
a broader framework that allows us to derive quantum-mechanical limits on the
precision to which a parameter---e.g., elapsed time---may be determined via
arbitrary data analysis of arbitrary measurements on identically prepared
quantum systems. The limits are expressed as generalized Mandelstam-Tamm
uncertainty relations, which involve the operator that generates displacements
of the parameter---e.g., the Hamiltonian operator in the case of elapsed time.
This approach avoids entirely the problem of associating a Hermitian operator
with the parameter. We illustrate the general formalism, first, with
nonrelativistic uncertainty relations for spatial displacement and momentum,
harmonic-oscillator phase and number of quanta, and time and energy and,
second, with Lorentz-invariant uncertainty relations involving the displacement
and Lorentz-rotation parameters of the Poincar\'e group.Comment: 39 pages of text plus one figure; text formatted in LaTe
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A multimedia tutorial shell with qualitative assessment in biology
The project is developing methods to produce multimedia tutorials relatively quickly and cheaply, using a generic software shell suitable for any subject area. The shell is a version of one produced originally as part of the HEFC-funded TLTP initiative by the Biodiversity Consortium. Tutorials presented in the shell will provide the student with a structured learning experience that will allow their initial knowledge level or their knowledge acquisition and progress to be qualitatively and quantitatively assessed. Where areas of weakness are revealed by the assessment, students will be advised to study particular parts of the tutorial in order to improve their understanding
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