34,022 research outputs found
Decoherence of quantum gates based on Aharonov-Anandan phases in a multistep scheme
We study quantum decoherence of single-qubit and two-qubit Aharonov-Anandan
(AA) geometric phase gates realized in a multistep scheme. Each AA gate is also
compared with the dynamical phase gate performing the same unitary
transformation within the same time period and coupled with the same
environment, which is modeled as harmonic oscillators. It is found that the
fidelities and the entanglement protection of the AA phase gates are enhanced
by the states being superpositions of different eigenstates of the
environmental coupling, and the noncommutativity between the qubit interaction
and the environmental coupling.Comment: 7 pages, published in EP
Formalizing Abstract Algebra in Constructive Set Theory
We present a machine-checked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with a binary operation is a group or not, and derive all properties of groups constructively from these inference rules as well as the axioms of the set theory. The formalization of all other concepts in abstract algebra is based on that of the group. We give an example of a formalization of a concrete group, the Klein 4-group
Recent works on the Strauss conjecture
In this review paper, we summarize the current state-of-art on the Strauss
conjecture with nontrapping obstacles. Among others, three essential estimates
are emphasized and presented: Morawetz-KSS estimates (also known as local
energy estimates), weighted Strichartz estimates and generalized Strichartz
estimates.Comment: 21 pages, no figures. No changes in content, but disable the usage of
the package showkey
Analysis and Comparison of Large Time Front Speeds in Turbulent Combustion Models
Predicting turbulent flame speed (the large time front speed) is a
fundamental problem in turbulent combustion theory. Several models have been
proposed to study the turbulent flame speed, such as the G-equations, the
F-equations (Majda-Souganidis model) and reaction-diffusion-advection (RDA)
equations. In the first part of this paper, we show that flow induced strain
reduces front speeds of G-equations in periodic compressible and shear flows.
The F-equations arise in asymptotic analysis of reaction-diffusion-advection
equations and are quadratically nonlinear analogues of the G-equations. In the
second part of the paper, we compare asymptotic growth rates of the turbulent
flame speeds from the G-equations, the F-equations and the RDA equations in the
large amplitude () regime of spatially periodic flows. The F and G equations
share the same asymptotic front speed growth rate; in particular, the same
sublinear growth law holds in cellular flows. Moreover, in two
space dimensions, if one of these three models (G-equation, F-equation and the
RDA equation) predicts the bending effect (sublinear growth in the large flow),
so will the other two. The nonoccurrence of speed bending is characterized by
the existence of periodic orbits on the torus and the property of their
rotation vectors in the advective flow fields. The cat's eye flow is discussed
as a typical example of directional dependence of the front speed bending. The
large time front speeds of the viscous F-equation have the same growth rate as
those of the inviscid F and G-equations in two dimensional periodic
incompressible flows.Comment: 42 page
Local distinguishability of orthogonal 2\otimes3 pure states
We present a complete characterization for the local distinguishability of
orthogonal pure states except for some special cases of three
states. Interestingly, we find there is a large class of four or three states
that are indistinguishable by local projective measurements and classical
communication (LPCC) can be perfectly distinguishable by LOCC. That indicates
the ability of LOCC for discriminating states is strictly more
powerful than that of LPCC, which is strikingly different from the case of
multi-qubit states. We also show that classical communication plays a crucial
role for local distinguishability by constructing a class of
states which require at least rounds of classical
communication in order to achieve a perfect local discrimination.Comment: 10 pages (revtex4), no figures. This is only a draft. It will be
replaced with a revised version soon. Comments are welcom
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