arXiv subjects

Lin Chen

Publications and source records attributed to Lin Chen.

At least 487 records · Page 27Linked to original sources

arXiv2017

Orthogonal product bases of four qubits

An orthogonal product basis (OPB) of a finite-dimensional Hilbert space $H=H_1\otimes H_2\otimes\cdots\otimes H_n$ is an orthonormal basis of $H$ consisting of product vectors $x_1\otimes x_2\otimes\cdots\otimes x_n$. We show that the problem of classifying the OPBs of an $n$-qubit system can be reduced to a purely combinatorial problem. We solve this combinatorial problem in the case of four qubits and obtain 33 multiparameter families of OPBs. Each OPB of four qubits is equivalent, under local unitary operations and qubit permutations, to an OPB belonging to at least one of these families.

quant-ph↗

arXiv2017

Submodular Variational Inference for Network Reconstruction

In real-world and online social networks, individuals receive and transmit information in real time. Cascading information transmissions (e.g. phone calls, text messages, social media posts) may be understood as a realization of a diffusion process operating on the network, and its branching path can be represented by a directed tree. The process only traverses and thus reveals a limited portion of the edges. The network reconstruction/inference problem is to infer the unrevealed connections. Most existing approaches derive a likelihood and attempt to find the network topology maximizing the likelihood, a problem that is highly intractable. In this paper, we focus on the network reconstruction problem for a broad class of real-world diffusion processes, exemplified by a network diffusion scheme called respondent-driven sampling (RDS). We prove that under realistic and general models of network diffusion, the posterior distribution of an observed RDS realization is a Bayesian log-submodular model.We then propose VINE (Variational Inference for Network rEconstruction), a novel, accurate, and computationally efficient variational inference algorithm, for the network reconstruction problem under this model. Crucially, we do not assume any particular probabilistic model for the underlying network. VINE recovers any connected graph with high accuracy as shown by our experimental results on real-life networks.

cs.LG↗

arXiv2017

Mutually unbiased bases in dimension six containing a product-vector basis

Excluding the existence of four MUBs in $\bbC^6$ is an open problem in quantum information. We investigate the number of product vectors in the set of four mutually unbiased bases (MUBs) in dimension six, by assuming that the set exists and contains a product-vector basis. We show that in most cases the number of product vectors in each of the remaining three MUBs is at most two. We further construct the exceptional case in which the three MUBs respectively contain at most three, two and two product vectors. We also investigate the number of vectors mutually unbiased to an orthonormal basis.

quant-ph↗

arXiv2017

Probing Transverse Momentum Broadening via Dihadron and Hadron-jet Angular Correlations in Relativistic Heavy-ion Collisions

Dijet, dihadron, hadron-jet angular correlations have been reckoned as important probes of the transverse momentum broadening effects in relativistic nuclear collisions. When a pair of high-energy jets created in hard collisions traverse the quark-gluon plasma produced in heavy-ion collisions, they become de-correlated due to the vacuum soft gluon radiation associated with the Sudakov logarithms and the medium-induced transverse momentum broadening. For the first time, we employ the systematical resummation formalism and establish a baseline calculation to describe the dihadron and hadron-jet angular correlation data in $pp$ and peripheral $AA$ collisions where the medium effect is negligible. We demonstrate that the medium-induced broadening $\langle p_\perp^2\rangle$ and the so-called jet quenching parameter $\hat q$ can be extracted from the angular de-correlations observed in $AA$ collisions. A global $χ^2$ analysis of dihadron and hadron-jet angular correlation data renders the best fit $\langle p_\perp^2 \rangle \sim 13~\textrm{GeV}^2$ for a quark jet at RHIC top energy. Further experimental and theoretical efforts along the direction of this work shall significantly advance the quantitative understanding of transverse momentum broadening and help us acquire unprecedented knowledge of jet quenching parameter in relativistic heavy-ion collisions.

hep-ph↗

arXiv2017

On the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges

For a molecular graph, the first multiplicative Zagreb index $Π_1$ is equal to the product of the square of the degree of the vertices, while the second multiplicative Zagreb index $Π_2$ is equal to the product of the endvertex degree of each edge over all edges. Denote by $\mathbb{G}_{n,k}$ the set of graphs with $n$ vertices and $k$ cut edges. In this paper, we explore graphs in terms of a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges are provided. Furthermore, we characterize graphs with the largest and smallest $Π_1(G)$ and $Π_2(G)$ in $\mathbb{G}_{n,k}$, and our results extend and enrich some known conclusions.

math.CO↗

arXiv2017

On the Mutual Information in Conformal Field Theory

In this work, we study the universal behaviors in the mutual information of two disjoint spheres in a conformal field theory(CFT). By using the operator product expansion of the spherical twist operator in terms of the conformal family, we show that the large distance expansion of the mutual information can be cast in terms of the conformal blocks. We develop the $1/n$ prescription to compute the coefficients before the conformal blocks. For a single conformal family, the leading nonvanishing contribution to the mutual information comes from the bilinear operators. We show that the coefficients of these operators take universal forms and such universal behavior persists in the bilinear operators with derivatives as well. Consequently the first few leading order contributions to the mutual information in CFT take universal forms. To illustrate our framework, we discuss the free scalars and free fermions in various dimensions. For the free scalars, we compute the mutual information to the next-to-leading order and find good agreement with the improved numerical lattice result. For the free fermion, we compute the leading order result, which is of universal form, and find the good match with the numerical study. Our formalism could be applied to any CFT potentially.

hep-th↗

arXiv2017

On various (strong) rainbow connection numbers of graphs

An edge-coloured path is \emph{rainbow} if all the edges have distinct colours. For a connected graph $G$, the \emph{rainbow connection number} $rc(G)$ is the minimum number of colours in an edge-colouring of $G$ such that, any two vertices are connected by a rainbow path. Similarly, the \emph{strong rainbow connection number} $src(G)$ is the minimum number of colours in an edge-colouring of $G$ such that, any two vertices are connected by a rainbow geodesic (i.e., a path of shortest length). These two concepts of connectivity in graphs were introduced by Chartrand et al.~in 2008. Subsequently, vertex-coloured versions of both parameters, $rvc(G)$ and $srvc(G)$, and a total-coloured version of the rainbow connection number, $trc(G)$, were introduced. In this paper we introduce the strong total rainbow connection number $strc(G)$, which is the version of the strong rainbow connection number using total-colourings. Among our results, we will determine the strong total rainbow connection numbers of some special graphs. We will also compare the six parameters, by considering how close and how far apart they can be from one another. In particular, we will characterise all pairs of positive integers $a$ and $b$ such that, there exists a graph $G$ with $trc(G)=a$ and $strc(G)=b$, and similarly for the functions $rvc$ and $srvc$.

math.CO↗

arXiv2017

On extremal multiplicative Zagreb indices of trees with given number of vertices of maximum degree

The first multiplicative Zagreb index of a graph $G$ is the product of the square of every vertex degree, while the second multiplicative Zagreb index is the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore the trees in terms of given number of vertices of maximum degree. The maximum and minimum values of $\prod_1(G) $ and $\prod_2(G) $ of trees with arbitrary number of maximum degree are provided. In addition, the corresponding extremal graphs are characterized.

math.CO↗

arXiv2017

On the NP-hardness of scheduling with time restrictions

In a recent paper, Braun, Chung and Graham [1] have addressed a single-processor scheduling problem with time restrictions. Given a fixed integer $B \geq 2$, there is a set of jobs to be processed by a single processor subject to the following B-constraint. For any real $x$, no unit time interval $[x, x+1)$ is allowed to intersect more than $B$ jobs. The problem has been shown to be NP-hard when $B$ is part of the input and left as an open question whether it remains NP-hard or not if $B$ is fixed [1, 5, 7]. This paper contributes to answering this question that we prove the problem is NP-hard even when $B=2$. A PTAS is also presented for any constant $B \geq 2$.

cs.DS↗

arXiv2017

Scheduling Maintenance Jobs in Networks

We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.

cs.DS↗

arXiv2016

Lower and upper bounds for entanglement of Rényi-$α$ entropy

Entanglement Rényi-$α$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $α$ tends to 1. We derive analytical lower and upper bounds for the entanglement Rényi-$α$ entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rényi-$α$ entropy and some other entanglement measures.

quant-ph↗

arXiv2016

Dijet Asymmetry in the Resummation Improved Perturbative QCD Approach

We develop the first systematic theoretical approach to dijet asymmetries in hadron-hadron collisions based on the perturbative QCD (pQCD) expansion and the Sudakov resummation formalism. We find that the pQCD calculation at next-to-leading order is indispensable to describe the experimental data, while the Sudakov resummation formalism is vital near the end points where the pQCD expansion fails to converge due to the appearance of large Sudakov logarithms. Utilizing our resummation improved pQCD approach, we obtain good agreement with the most up-to-date fully corrected ATLAS data on dijet asymmetry in $pp$ collisions. Combining with the BDMPS jet energy loss formalism, we extract the value of jet transport coefficient $\hat{q}_0 \sim 2$-$6~\textrm{GeV}^2/\textrm{fm}$ for the quark-gluon-plasma created in $PbPb$ collisions at 2.76A TeV. This work paves the way for a more complete and deeper understanding of the properties of strongly-coupled QCD medium via the studies of dijet asymmetries in relativistic heavy-ion collisions.

hep-ph↗

arXiv2016

Near-Optimal Active Learning of Halfspaces via Query Synthesis in the Noisy Setting

In this paper, we consider the problem of actively learning a linear classifier through query synthesis where the learner can construct artificial queries in order to estimate the true decision boundaries. This problem has recently gained a lot of interest in automated science and adversarial reverse engineering for which only heuristic algorithms are known. In such applications, queries can be constructed de novo to elicit information (e.g., automated science) or to evade detection with minimal cost (e.g., adversarial reverse engineering). We develop a general framework, called dimension coupling (DC), that 1) reduces a d-dimensional learning problem to d-1 low dimensional sub-problems, 2) solves each sub-problem efficiently, 3) appropriately aggregates the results and outputs a linear classifier, and 4) provides a theoretical guarantee for all possible schemes of aggregation. The proposed method is proved resilient to noise. We show that the DC framework avoids the curse of dimensionality: its computational complexity scales linearly with the dimension. Moreover, we show that the query complexity of DC is near optimal (within a constant factor of the optimum algorithm). To further support our theoretical analysis, we compare the performance of DC with the existing work. We observe that DC consistently outperforms the prior arts in terms of query complexity while often running orders of magnitude faster.

cs.AI↗

arXiv2016

Estimating the Size of a Large Network and its Communities from a Random Sample

Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = (V;E) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W and letting G(W) be the induced subgraph in G of the vertices in W. In addition to G(W), we observe the total degree of each sampled vertex and its block membership. Given this partial information, we propose an efficient PopULation Size Estimation algorithm, called PULSE, that correctly estimates the size of the whole population as well as the size of each community. To support our theoretical analysis, we perform an exhaustive set of experiments to study the effects of sample size, K, and SBM model parameters on the accuracy of the estimates. The experimental results also demonstrate that PULSE significantly outperforms a widely-used method called the network scale-up estimator in a wide variety of scenarios. We conclude with extensions and directions for future work.

stat.ML↗

arXiv2016

Entangling and assisted entangling power of bipartite unitary operations

Nonlocal unitary operations can create quantum entanglement between distributed particles, and the quantification of created entanglement is a hard problem. It corresponds to the concepts of entangling and assisted entangling power when the input states are, respectively, product and arbitrary pure states. We analytically derive them for Schmidt-rank-two bipartite unitary and some complex bipartite permutation unitaries. In particular, the entangling power of permutation unitary of Schmidt rank three can take only one of two values: $\log_2 9 - 16/9$ or $\log_2 3$ ebits. The entangling power, assisted entangling power and disentangling power of $2\times d_B$ permutation unitaries of Schmidt rank four are all $2$ ebits. These quantities are also derived for generalized Clifford operators. We further show that any bipartite permutation unitary of Schmidt rank greater than two has entangling power greater than $1.223$ ebits. We construct the generalized controlled-NOT (CNOT) gates whose assisted entangling power reaches the maximum. We quantitatively compare the entangling power and assisted entangling power for general bipartite unitaries, and study their connection to the disentangling power. We also propose a probabilistic protocol for implementing bipartite unitaries.

quant-ph↗

arXiv2016

The existence of the graphs that have exactly two main eigenvalues

An eigenvalue of a graph $G$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. It is well known that a graph $G$ has exactly two main eigenvalues if and only if there exists a unique pair of integers $a$ and $b$ such that $\sum_{u\in N(v)}d(u)=ad(v)+b$ for every vertex $v\in V(G)$. We collect such connected graph $G$ in the set $\mathscr{G}(a,b)$. In this paper, we mainly focus to the existence of such $a$ and $b$, and give the necessary and sufficient condition for $\mathscr{G}(a,b)\neq\emptyset$. In addition, we give the bound for the vertex degrees of $G\in\mathscr{G}(a,b)$ and use the bound to characterize the graphs in $\mathscr{G}(a,b)$ for some feasible pairs $(a,b)$.

math.CO↗

arXiv2016

Schmidt number of bipartite and multipartite states under local projections

The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation in quantum physics. We investigate the relation between the Schmidt numbers of bipartite states and their projected states. We show that there exist bipartite positive-partial-transpose (PPT) entangled states of any given Schmidt number. We further construct the notion of joint Schmidt number for multipartite states, and its relation with the Schmidt number of bipartite reduced density operators.

quant-ph↗

arXiv2016

Precise tuning of the Curie temperature of (Ga,Mn)As-based magnetic semiconductors by hole compensation: Support for valence-band ferromagnetism

For the prototype diluted ferromagnetic semiconductor (Ga,Mn)As, there is a fundamental concern about the electronic states near the Fermi level, i.e., whether the Fermi level resides in a well-separated impurity band derived from Mn doping (impurity-band model) or in the valence band that is already merged with the Mn-derived impurity band (valence-band model). We investigate this question by carefully shifting the Fermi level by means of carrier compensation. We use helium-ion implantation, a standard industry technology, to precisely compensate the hole doping of GaAs-based diluted ferromagnetic semiconductors while keeping the Mn concentration constant. We monitor the change of Curie temperature ($T_C$) and conductivity. For a broad range of samples including (Ga,Mn)As and (Ga,Mn)(As,P) with various Mn and P concentrations, we observe a smooth decrease of $T_C$ with carrier compensation over a wide temperature range while the conduction is changed from metallic to insulating. The existence of $T_C$ below 10\,K is also confirmed in heavily compensated samples. Our experimental results are naturally explained within the valence-band picture.

cond-mat.mtrl-sci↗