3,669 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
Universal state inversion and concurrence in arbitrary dimensions
Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for
the entanglement of formation of two qubits in terms of what he calls the
concurrence of the joint density operator. Wootters's concurrence is defined
with the help of the superoperator that flips the spin of a qubit. We
generalize the spin-flip superoperator to a "universal inverter," which acts on
quantum systems of arbitrary dimension, and we introduce the corresponding
concurrence for joint pure states of (D1 X D2) bipartite quantum systems. The
universal inverter, which is a positive, but not completely positive
superoperator, is closely related to the completely positive universal-NOT
superoperator, the quantum analogue of a classical NOT gate. We present a
physical realization of the universal-NOT superoperator.Comment: Revtex, 25 page
Quantum-mechanical model for continuous position measurements
We present an idealized model for a sequence of position measurements, and we then take an appropriate limit in which the measurements become continuous. The measurements lead to fluctuations without systematic dissipation, and they rapidly destroy off-diagonal terms in the position basis; thus the pointer basis is position. A modification of the model incorporates systematic dissipation via a feedback mechanism; in the modified model there is no decay of off-diagonal coherence in the position basis
Teleportation fidelity as a probe of sub-Planck phase-space structure
We investigate the connection between sub-Planck structure in the Wigner
function and the output fidelity of continuous-variable teleportation
protocols. When the teleporting parties share a two-mode squeezed state as an
entangled resource, high fidelity in the output state requires a squeezing
large enough that the smallest sub-Planck structures in an input pure state are
teleported faithfully. We formulate this relationship, which leads to an
explicit relation between the fine-scale structure in the Wigner function and
large-scale extent of the Wigner function, and we treat specific examples,
including coherent, number, and random states and states produced by chaotic
dynamics. We generalize the pure-state results to teleportation of mixed
states.Comment: 19 pages, 5 figure
Information Otherwise Unknowable: Carpenter as a Window into the Judicial Decision-Making Process
In 2017, the United States Supreme Court decided Carpenter v. United States, a landmark decision that expanded the protection of the Fourth Amendment to cell phone location records. In addition to its doctrinal importance, Carpenter—a 5–4 decision that was not split cleanly along ideological lines, and that featured a myriad of theories of Fourth Amendment jurisprudence—also holds great insight as to how judges decide cases, particularly at the level of the Supreme Court. This Article explores the process of judicial decision-making by using Carpenter as a springboard for analysis. Relying on the vast research, both legal and psychological, on judicial decision-making, this Article explores the explicit and implicit factors that influence judges and then analyzes these factors in the context of the Carpenter decision
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