170,033 research outputs found
Intense isolated few-cycle attosecond XUV pulses from overdense plasmas driven by tailored laser pulses
A method to generate an intense isolated few-cycle attosecond XUV pulse is
demonstrated using particle-in-cell simulations. When a tailored laser pulse
with a sharp edge irradiates a foil target, a strong transverse net current can
be excited, which emits a few-cycle XUV pulse from the target rear side. The
isolated pulse is ultrashort in the time domain with a duration of several
hundred attoseconds. It also has a narrow bandwidth in the spectral domain
compared to other XUV sources of high-order harmonics. It has most energy
confined around the plasma frequency and no low-harmonic orders below the
plasma frequency. It is also shown that XUV pulse of peak field strength up to
V can be produced. Without the need for
pulse selecting and spectral filtering, such an intense few-cycle XUV pulse is
better suited to a number of applications.Comment: 9 pages,5 figures; Published in Optics Expres
Some remarks for the Akivis algebras and the Pre-Lie algebras
In this paper, by using the Composition-Diamond lemma for non-associative
algebras invented by A. I. Shirshov in 1962, we give Gr\"{o}bner-Shirshov bases
for free Pre-Lie algebras and the universal enveloping non-associative algebra
of an Akivis algebra, respectively. As applications, we show I.P. Shestakov's
result that any Akivis algebra is linear and D. Segal's result that the set of
all good words in forms a linear basis of the free Pre-Lie algebra
generated by the set . For completeness, we give the details of
the proof of Shirshov's Composition-Diamond lemma for non-associative algebras
Nonlocal and controlled unitary operators of Schmidt rank three
Implementing nonlocal unitary operators is an important and hard question in
quantum computing and cryptography. We show that any bipartite nonlocal unitary
operator of Schmidt rank three on the -dimensional system is
locally equivalent to a controlled unitary when is at most three. This
operator can be locally implemented assisted by a maximally entangled state of
Schmidt rank . We further show that stochastic-equivalent
nonlocal unitary operators are indeed locally equivalent, and propose a
sufficient condition on which nonlocal and controlled unitary operators are
locally equivalent. We also provide the solution to a special case of a
conjecture on the ranks of multipartite quantum states.Comment: 14 pages, 1 figur
Entanglement cost and entangling power of bipartite unitary and permutation operators
It is known that any bipartite unitary operator of Schmidt rank three is
equivalent to a controlled unitary under local unitaries. We propose a standard
form of such operators. Using the form we improve the upper bound for the
entanglement cost to implement such operators under local operations and
classical communications (LOCC), and provide a corresponding protocol. A part
of our protocol is based on a recursive-control protocol which is helpful for
implementing other unitary operators. We show that any bipartite permutation
unitary of Schmidt rank three can be implemented using LOCC and two ebits. We
give two protocols for implementing bipartite permutation unitaries of any
Schmidt rank , and showed that one of the protocol uses ebits of
entanglement and bits of classical communication, while these two types
of costs for the other protocol scale as but the actual values are
smaller for all . Based on this we obtain upper bounds of the number of
nonlocal CNOT gates needed to implement bipartite classical reversible maps
using classical circuits under two different conditions. We also quantify the
entangling power of bipartite permutation unitaries of Schmidt rank two and
three. We show that they are respectively ebit and some value between
and ebits.Comment: 27 pages, 2 figures. Minor improvements and corrections compared to
v3. Almost the same as the published version except the numbering of theorems
and lemmas, et
Flexible and tunable silicon photonic circuits on plastic substrates
Flexible microelectronics has shown tremendous promise in a broad spectrum of
applications, especially those that cannot be addressed by conventional
microelectronics in rigid materials and constructions1-3. These unconventional
yet important applications range from flexible consumer electronics to
conformal sensor arrays and biomedical devices. A recent successful paradigm
shift in implementing flexible electronics is to physically transfer and bond
highly integrated devices made in high-quality, crystalline semiconductor
materials on to plastic materials4-8. Here we demonstrate a flexible form of
silicon photonics on plastic substrates using the transfer-and-bond fabrication
method. Photonic circuits including interferometers and resonators have been
transferred onto flexible plastic substrates with preserved functionalities and
performance. By mechanically deforming the flexible substrates, the optical
characteristics of the devices can be tuned reversibly over a remarkably large
range. The demonstration of the new flexible photonic system based on the
silicon-on-plastic (SOP) material platform could open the door to a plethora of
novel applications, including tunable photonics, optomechanical sensors and
bio-mechanical and bio-photonic probes.Comment: Part of this work was presented at 2012 CLEO conference on May 8th,
201
Unsupervised Sequence Classification using Sequential Output Statistics
We consider learning a sequence classifier without labeled data by using
sequential output statistics. The problem is highly valuable since obtaining
labels in training data is often costly, while the sequential output statistics
(e.g., language models) could be obtained independently of input data and thus
with low or no cost. To address the problem, we propose an unsupervised
learning cost function and study its properties. We show that, compared to
earlier works, it is less inclined to be stuck in trivial solutions and avoids
the need for a strong generative model. Although it is harder to optimize in
its functional form, a stochastic primal-dual gradient method is developed to
effectively solve the problem. Experiment results on real-world datasets
demonstrate that the new unsupervised learning method gives drastically lower
errors than other baseline methods. Specifically, it reaches test errors about
twice of those obtained by fully supervised learning.Comment: All authors contributed equally to the paper. 17 pages, 7 figures and
2 table
Self-dual binary codes from small covers and simple polytopes
We explore the connection between simple polytopes and self-dual binary codes
via the theory of small covers. We first show that a small cover over a
simple -polytope produces a self-dual code in the sense of Kreck-Puppe
if and only if is -colorable and is odd. Then we show how to
describe such a self-dual binary code in terms of the combinatorial information
of . Moreover, we can define a family of binary codes
, , from an arbitrary simple -polytope
. We will give some necessary and sufficient conditions for
to be a self-dual code. A spinoff of our study of such
binary codes gives some new ways to judge whether a simple -polytope
is -colorable in terms of the associated binary codes .
In addition, we prove that the minimum distance of the self-dual binary code
obtained from a -colorable simple -polytope is always .Comment: 27 pages, 5 figure
BERTSel: Answer Selection with Pre-trained Models
Recently, pre-trained models have been the dominant paradigm in natural
language processing. They achieved remarkable state-of-the-art performance
across a wide range of related tasks, such as textual entailment, natural
language inference, question answering, etc. BERT, proposed by Devlin et.al.,
has achieved a better marked result in GLUE leaderboard with a deep transformer
architecture. Despite its soaring popularity, however, BERT has not yet been
applied to answer selection. This task is different from others with a few
nuances: first, modeling the relevance and correctness of candidates matters
compared to semantic relatedness and syntactic structure; second, the length of
an answer may be different from other candidates and questions. In this paper.
we are the first to explore the performance of fine-tuning BERT for answer
selection. We achieved STOA results across five popular datasets, demonstrating
the success of pre-trained models in this task
Entanglement of stabilizer codewords
The geometric measure, the logarithmic robustness and the relative entropy of
entanglement are proved to be equal for a stabilizer quantum codeword. The
entanglement upper and lower bounds are determined with the generators of code.
The entanglement of dual-containing CSS codes, Gottesman codes and the related
codes are given. An iterative algorithm is developed to determine the exact
value of the entanglement when the two bounds are not equal.Comment: 9 page
A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states
With a two step optimization method of entanglement witness, we analytically
propose a set of necessary and sufficient entanglement criteria for four qubit
symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set
contains four criteria. Two of them are linear with density matrix elements.
The other two criteria are nonlinear with density matrix elements. The
criterion set has a nest structure. A proper subset of the criteria is
necessary and sufficient for the entanglement of a proper subset of the states.
We illustrate the nest structure of criterion set with the general Werner state
set and its superset the highly symmetric GHZ diagonal state set, they are
subsets of the symmetric GHZ diagonal state set.Comment: 10 pages, 3 figure
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