arXiv subjects

Lin Chen

Publications and source records attributed to Lin Chen.

At least 487 records · Page 27Linked to original sources

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↗

arXiv2016

The Birkhoff theorem for unitary matrices of arbitrary dimensions

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimension.

math-ph↗

arXiv2016

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.

quant-ph↗

arXiv2016

On Diffusion-restricted Social Network: A Measurement Study of WeChat Moments

WeChat is a mobile messaging application that has 549 million active users as of Q1 2015, and "WeChat Moments" (WM) serves its social-networking function that allows users to post/share links of web pages. WM differs from the other social networks as it imposes many restrictions on the information diffusion process to mitigate the information overload. In this paper, we conduct a measurement study on information diffusion in the WM network by crawling and analyzing the spreading statistics of more than 160,000 pages that involve approximately 40 million users. Specifically, we identify the relationship of the number of posted pages and the number of views, the diffusion path length, the similarity and distribution of users' locations as well as their connections with the GDP of the users' province. For each individual WM page, we measure its temporal characteristics (e.g., the life time, the popularity within a time period); for each individual user, we evaluate how many of, or how likely, one's friends will view his posted pages. Our results will help the business to decide when and how to release the marketing pages over WM for better publicity.

cs.CY↗

arXiv2016

Length filtration of the separable states

We investigate the separable states $\r$ of an arbitrary multipartite quantum system with Hilbert space $\cH$ of dimensionin $d$. The length $L(\r)$ of $\r$ is defined as the smallest number of pure product states having $\r$ as their mixture. The length filtration of the set of separable states, $\cS$, is the increasing chain $\emptyset\subset\cS'_1\subseteq\cS'_2\subseteq\cdots$, where $\cS'_i=\{\r\in\cS:L(\r)\le i\}$. We define the maximum length, $L_{\rm max}=\max_{\r\in\cS} L(\r)$, critical length, $L_{\rm crit}$, and yet another special length, $L_c$, which was defined by a simple formula in one of our previous papers. The critical length indicates the first term in the length filtrartion whose dimension is equal to $\dim\cS$. We show that in general $d\le L_c\le L_{\rm crit}\le L_{\rm max}\le d^2$. We conjecture that the equality $L_{\rm crit}=L_c$ holds for all finite-dimensional multipartite quantum systems. Our main result is that $L_{\rm crit}=L_c$ for the bipartite systems having a single qubit as one of the parties. This is accomplished by computing the rank of the Jacobian matrix of a suitable map having $\cS$ as its range.

quant-ph↗

arXiv2016

Non-positive-partial-transpose quantum states of rank four are distillable

We show that any bipartite quantum state of rank four is distillable, when the partial transpose of the state has at least one negative eigenvalue, i.e., the state is NPT. For this purpose we prove that if the partial transpose of a two-qutrit NPT state has two non-positive eigenvalues, then the state is distillable. We further construct a parametrized two-qutrit NPT entangled state of rank five which is not 1-distillable, and show that it is not $n$-distillable for any given $n$ when the parameter is sufficiently small. This state has the smallest rank among all 1-undistillable NPT states. We conjecture that the state is not distillable.

quant-ph↗

arXiv2016

Skolem Sequence Based Self-adaptive Broadcast Protocol in Cognitive Radio Networks

The base station (BS) in a multi-channel cognitive radio (CR) network has to broadcast to secondary (or unlicensed) receivers/users on more than one broadcast channels via channel hopping (CH), because a single broadcast channel can be reclaimed by the primary (or licensed) user, leading to broadcast failures. Meanwhile, a secondary receiver needs to synchronize its clock with the BS's clock to avoid broadcast failures caused by the possible clock drift between the CH sequences of the secondary receiver and the BS. In this paper, we propose a CH-based broadcast protocol called SASS, which enables a BS to successfully broadcast to secondary receivers over multiple broadcast channels via channel hopping. Specifically, the CH sequences are constructed on basis of a mathematical construct---the Self-Adaptive Skolem sequence. Moreover, each secondary receiver under SASS is able to adaptively synchronize its clock with that of the BS without any information exchanges, regardless of any amount of clock drift.

cs.NI↗

arXiv2016

The $k$-proper index of graphs

A tree $T$ in an edge-colored graph is a \emph{proper tree} if any two adjacent edges of $T$ are colored with different colors. Let $G$ be a graph of order $n$ and $k$ be a fixed integer with $2\leq k\leq n$. For a vertex set $S\subseteq V(G)$, a tree containing the vertices of $S$ in $G$ is called an \emph{$S$-tree}. An edge-coloring of $G$ is called a \emph{$k$-proper coloring} if for every set $S$ of $k$ vertices in $G$, there exists a proper $S$-tree in $G$. The \emph{$k$-proper index} of a nontrivial connected graph $G$, denoted by $px_k(G)$, is the smallest number of colors needed in a $k$-proper coloring of $G$. In this paper, some simple observations about $px_k(G)$ for a nontrivial connected graph $G$ are stated. Meanwhile, the $k$-proper indices of some special graphs are determined, and for every pair of positive integers $a$, $b$ with $2\leq a\leq b$, a connected graph $G$ with $px_k(G)=a$ and $rx_k(G)=b$ is constructed for each integer $k$ with $3\leq k\leq n$. Also, the graphs with $k$-proper index $n-1$ and $n-2$ are respectively characterized.

math.CO↗

arXiv2015

Finding Needles in a Haystack: Missing Tag Detection in Large RFID Systems

Radio frequency identification (RFID) technology has been widely used in missing tag detection to reduce and avoid inventory shrinkage. In this application, promptly finding out the missing event is of paramount importance. However, existing missing tag detection protocols cannot efficiently handle the presence of a large number of unexpected tags whose IDs are not known to the reader, which shackles the time efficiency. To deal with the problem of detecting missing tags in the presence of unexpected tags, this paper introduces a two-phase Bloom filter-based missing tag detection protocol (BMTD). The proposed BMTD exploits Bloom filter in sequence to first deactivate the unexpected tags and then test the membership of the expected tags, thus dampening the interference from the unexpected tags and considerably reducing the detection time. Moreover, the theoretical analysis of the protocol parameters is performed to minimize the detection time of the proposed BMTD and achieve the required reliability simultaneously. Extensive experiments are then conducted to evaluate the performance of the proposed BMTD. The results demonstrate that the proposed BMTD significantly outperforms the state-of-the-art solutions.

cs.OH↗

arXiv2015

New Results on Online Resource Minimization

We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this problem and derive various algorithms with small constant competitive ratios for interesting restricted problem variants. As the most important special case, we consider scheduling jobs with agreeable deadlines. We provide the first constant ratio competitive algorithm for the non-preemptive setting, which is of particular interest with regard to the known strong lower bound of n for the general problem. For the preemptive setting, we show that the natural algorithm LLF achieves a constant ratio for agreeable jobs, while for general jobs it has a lower bound of Omega(n^(1/3)). We also give an O(log n)-competitive algorithm for the general preemptive problem, which improves upon the known O(p_max/p_min)-competitive algorithm. Our algorithm maintains a dynamic partition of the job set into loose and tight jobs and schedules each (temporal) subset individually on separate sets of machines. The key is a characterization of how the decrease in the relative laxity of jobs influences the optimum number of machines. To achieve this we derive a compact expression of the optimum value, which might be of independent interest. We complement the general algorithmic result by showing lower bounds that rule out that other known algorithms may yield a similar performance guarantee.

cs.DS↗

arXiv2015

Seeing the Unseen Network: Inferring Hidden Social Ties from Respondent-Driven Sampling

Learning about the social structure of hidden and hard-to-reach populations --- such as drug users and sex workers --- is a major goal of epidemiological and public health research on risk behaviors and disease prevention. Respondent-driven sampling (RDS) is a peer-referral process widely used by many health organizations, where research subjects recruit other subjects from their social network. In such surveys, researchers observe who recruited whom, along with the time of recruitment and the total number of acquaintances (network degree) of respondents. However, due to privacy concerns, the identities of acquaintances are not disclosed. In this work, we show how to reconstruct the underlying network structure through which the subjects are recruited. We formulate the dynamics of RDS as a continuous-time diffusion process over the underlying graph and derive the likelihood for the recruitment time series under an arbitrary recruitment time distribution. We develop an efficient stochastic optimization algorithm called RENDER (REspoNdent-Driven nEtwork Reconstruction) that finds the network that best explains the collected data. We support our analytical results through an exhaustive set of experiments on both synthetic and real data.

cs.SI↗

arXiv2015

From Static to Dynamic Tag Population Estimation: An Extended Kalman Filter Perspective

Tag population estimation has recently attracted significant research attention due to its paramount importance on a variety of radio frequency identification (RFID) applications. However, most, if not all, of existing estimation mechanisms are proposed for the static case where tag population remains constant during the estimation process, thus leaving the more challenging dynamic case unaddressed, despite the fundamental importance of the latter case on both theoretical analysis and practical application. In order to bridge this gap, %based on \textit{dynamic framed-slotted ALOHA} (DFSA) protocol, we devote this paper to designing a generic framework of stable and accurate tag population estimation schemes based on Kalman filter for both static and dynamic RFID systems. %The objective is to devise estimation schemes and analyze the boundedness of estimation error. Technically, we first model the dynamics of RFID systems as discrete stochastic processes and leverage the techniques in extended Kalman filter (EKF) and cumulative sum control chart (CUSUM) to estimate tag population for both static and dynamic systems. By employing Lyapunov drift analysis, we mathematically characterise the performance of the proposed framework in terms of estimation accuracy and convergence speed by deriving the closed-form conditions on the design parameters under which our scheme can stabilise around the real population size with bounded relative estimation error that tends to zero with exponential convergence rate.

eess.SY↗

arXiv2015

Universal steering inequalities

We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint measurement problem. Based on the data-processing inequality for an extended Rényi relative entropy, we then introduce a family of universal steering inequalities, which detect steering much more efficiently than those inequalities known before. As illustrations, we show unbounded violation of a steering inequality for assemblages constructed from mutually unbiased bases and establish an interesting connection between maximally steerable assemblages and complete sets of mutually unbiased bases. We also provide a single steering inequality that can detect all bipartite pure states of full Schmidt rank. In the course of study, we generalize a number of results intimately connected to data-processing inequalities, which are of independent interest.

quant-ph↗

arXiv2015

Boundary of the set of separable states

Motivated by the separability problem in quantum systems $2\otimes4$, $3\otimes3$ and $2\otimes2\otimes2$, we study the maximal (proper) faces of the convex body, $S_1$, of normalized separable states in an arbitrary quantum system with finite-dimensional Hilbert space $H=H_1\otimes H_2\otimes\cdots\otimes H_n$. To any subspace $V$ of $H$ we associate a face $F_V$ of $S_1$ consisting of all states $ρ\in S_1$ whose range is contained in $V$. We prove that $F_V$ is a maximal face if and only if $V$ is a hyperplane. If $V$ is the hyperplane orthogonal to a product vector, we prove that $\dim F_V=d^2-1-\prod(2d_i-1)$, where $d_i$ is the dimension of $H_i$ and $d=\prod d_i$. We classify the maximal faces of $S_1$ in the cases $2\otimes2$ and $2\otimes3$. In particular we show that the minimum and the maximum dimension of maximal faces is 6 and 8 for $2\otimes2$, and 20 and 24 for $2\otimes3$. The boundary of $S_1$ is the union of all maximal faces. When $d>6$ we prove that there exist full states $ρ$ on the boundary, i.e., such that all partial transposes of $ρ$ (including $ρ$ itself) have rank $d$. K.-C. Ha and S.-K. Kye have recently constructed explicit such states in $2\times4$ and $3\otimes3$. In the latter case, they have also constructed a remarkable family of faces, depending on a real parameter $b>0$, $b\ne1$. Each face in the family is a 9-dimensional simplex and any interior point of the face is a full state. We construct suitable optimal entanglement witnesses (OEW) for these faces and analyze the three limiting cases $b=0,1,\infty$.

quant-ph↗

arXiv2015

Fidelity between a bipartite state and another one undergoing local unitary dynamics

The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing local unitary dynamics. The problems are related to the geometric measure of entanglement and the distillability problem. We show that the problems can be reduced to semi-definite programming optimization problems. We give close-form formulae of the fidelity when the two states are both pure states, or a pure product state and the Werner state. We explain from the point of view of local unitary actions that why the entanglement in Werner states is hard to accessible. For general mixed states, we give upper and lower bounds of the fidelity using tools such as affine fidelity, channels and relative entropy from information theory. We also investigate the power of local unitaries and quantification for the commutativity of quantum states, and the equivalence of the two optimization problems.

quant-ph↗