51,997 research outputs found
One-step error correction for multipartite polarization entanglement
We present two economical one-step error-correction protocols for
multipartite polarization-entangled systems in a Greenberger-Horne-Zeilinger
state. One uses spatial entanglement to correct errors in the polarization
entanglement of an N-photon system, resorting to linear optical elements. The
other uses frequency entanglement to correct errors in the polarization
entanglement of an N-photon system. The parties in quantum communication can
obtain a maximally entangled state from each N-photon system transmitted with
one step in these two protocols, and both of their success probabilities are
100%, in principle. That is, they both work in a deterministic way, and they do
not largely consume the less-entangled photon systems, which is far different
from conventional multipartite entanglement purification schemes. These
features may make these two protocols more useful for practical applications in
long-distance quantum communication.Comment: 8 pages, 2 figure
Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
We explore the robustness of universal dynamical scaling behavior in a
quantum system near criticality with respect to initialization in a large class
of states with finite energy. By focusing on a homogeneous XY quantum spin
chain in a transverse field, we characterize the non-equilibrium response under
adiabatic and sudden quench processes originating from a pure as well as a
mixed excited initial state, and involving either a regular quantum critical or
a multicritical point. We find that the critical exponents of the ground-state
quantum phase transition can be encoded in the dynamical scaling exponents
despite the finite energy of the initial state. In particular, we identify
conditions on the initial distribution of quasi-particle excitation which
ensure Kibble-Zurek scaling to persist. The emergence of effective thermal
equilibrium behavior following a sudden quench towards criticality is also
investigated, with focus on the long-time dynamics of the quasi-particle
excitation. For a quench to a regular quantum critical point, this observable
is found to behave thermally provided that the system is prepared at
sufficiently high temperature, whereas thermalization fails to occur in
quenches taking the system towards a multi-critical point. We argue that the
observed lack of thermalization originates in this case in the asymmetry of the
impulse region that is also responsible for anomalous multicritical dynamical
scaling.Comment: 18 pages, 13 eps color figures, published versio
Gr\"obner-Shirshov bases for Rota-Baxter algebras
In this paper, we establish the Composition-Diamond lemma for associative
nonunitary Rota-Baxter algebras with weight . As applications, we
obtain a linear basis of a free commutative Rota-Baxter algebra without unity
and show that every countably generated Rota-Baxter algebra with weight 0 can
be embedded into a two-generated Rota-Baxter algebra.Comment: 24 page
Rank-frequency relation for Chinese characters
We show that the Zipf's law for Chinese characters perfectly holds for
sufficiently short texts (few thousand different characters). The scenario of
its validity is similar to the Zipf's law for words in short English texts. For
long Chinese texts (or for mixtures of short Chinese texts), rank-frequency
relations for Chinese characters display a two-layer, hierarchic structure that
combines a Zipfian power-law regime for frequent characters (first layer) with
an exponential-like regime for less frequent characters (second layer). For
these two layers we provide different (though related) theoretical descriptions
that include the range of low-frequency characters (hapax legomena). The
comparative analysis of rank-frequency relations for Chinese characters versus
English words illustrates the extent to which the characters play for Chinese
writers the same role as the words for those writing within alphabetical
systems.Comment: To appear in European Physical Journal B (EPJ B), 2014 (22 pages, 7
figures
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