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 $8\times 10^{12}$ V$\mathrm{m}^{-1}$ 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 $X^{**}$ forms a linear basis of the free Pre-Lie algebra $PLie(X)$ generated by the set $X$. 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 $(d_A \times d_B)$-dimensional system is locally equivalent to a controlled unitary when $d_A$ is at most three. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank $r=\min\{d_A^2,d_B\}$. 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 $r$, and showed that one of the protocol uses $O(r)$ ebits of entanglement and $O(r)$ bits of classical communication, while these two types of costs for the other protocol scale as $O(r\log r)$ but the actual values are smaller for all $r<1100$. 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 $1$ ebit and some value between $\log_2 9 - 16/9$ and $\log_2 3$ 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 $M^n$ over a simple $n$-polytope $P^n$ produces a self-dual code in the sense of Kreck-Puppe if and only if $P^n$ is $n$-colorable and $n$ is odd. Then we show how to describe such a self-dual binary code in terms of the combinatorial information of $P^n$. Moreover, we can define a family of binary codes $\mathfrak{B}_k(P^n)$, $0\leq k\leq n$, from an arbitrary simple $n$-polytope $P^n$. We will give some necessary and sufficient conditions for $\mathfrak{B}_k(P^n)$ to be a self-dual code. A spinoff of our study of such binary codes gives some new ways to judge whether a simple $n$-polytope $P^n$ is $n$-colorable in terms of the associated binary codes $\mathfrak{B}_k(P^n)$. In addition, we prove that the minimum distance of the self-dual binary code obtained from a $3$-colorable simple $3$-polytope is always $4$.Comment: 27 pages, 5 figure

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

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