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Lin Chen

Publications and source records attributed to Lin Chen.

At least 523 records · Page 29Linked to original sources
arXiv2014

Non-zero total correlation means non-zero quantum correlation

We investigated the super quantum discord based on weak measurements. The super quantum discord is an extension of the standard quantum discord defined by projective measurements and also describes the quantumness of correlations. We provide some equivalent conditions for zero super quantum discord by using quantum discord, classical correlation and mutual information. In particular, we find that the super quantum discord is zero only for product states, which have zero mutual information. This result suggests that non-zero correlations can always be detected using the quantum correlation with weak measurements. As an example, we present the assisted state-discrimination method.

quant-ph↗
arXiv2014

Spin transport and accumulation in the persistent photoconductor Al$_{0.3}$Ga$_{0.7}$As

Electrical spin transport and accumulation have been measured in highly Si doped Al0.3Ga0.7As utilizing a lateral spin transport device. Persistent photoconductivity allows for the tuning of the effective carrier density of the channel material in situ via photodoping. Hanle effect measurements are completed at various carrier densities and the measurements yield spin lifetimes on the order of nanoseconds, an order of magnitude smaller than in bulk GaAs. These measurements illustrate that this methodology can be used to obtain a detailed description of how spin lifetimes depend on carrier density in semiconductors across the metal-insulator transition.

cond-mat.mtrl-sci↗
arXiv2014

Bias current dependence of the spin lifetime in insulating Al$_{0.3}$Ga$_{0.7}$As

The spin lifetime and Hanle signal amplitude dependence on bias current has been investigated in insulating Al$_{0.3}$Ga$_{0.7}$As:Si using a three-terminal Hanle effect geometry. The amplitudes of the Hanle signals are much larger for forward bias than for reverse bias, although the spin lifetimes found are statistically equivalent. The spin resistance-area product shows a strong increase with bias current for reverse bias and small forward bias until 150 $μ$A, beyond which a weak dependence is observed. The spin lifetimes diminish substantially with increasing bias current. The dependence of the spin accumulation and lifetime diminish only moderately with temperature from 5 K to 30 K.

cond-mat.mtrl-sci↗
arXiv2014

Mc-Dis: A Heterogeneous Neighbor Discovery Protocol for Multi-channel Wireless Networks

In distributed wireless networks, neighbor discovery is one of the bootstrapping primitives in supporting many important network functionalities. Existing neighbor discovery protocols mostly assume a single-channel network model and can only support a subset of duty cycles, thus limiting the energy conservation levels of wireless devices. In this paper, we study the neighbor discovery problem in multi-channel networks where the wireless nodes have heterogeneous duty cycles, asynchronous clocks and asymmetrical channel perceptions, which we formulate as heterogeneous neighbor discovery problem. We first establish a performance bound for any neighbor discovery protocol by relating the two performance metrics, discovery delay and diversity. We then present the design, analysis and evaluation of Mc-Dis, a multi-channel neighbor discovery protocol that can support can practically support almost all duty cycles and guarantee discovery on every channel in multichannel networks even when nodes have asynchronous clocks and asymmetrical channel perceptions.

cs.NI↗
arXiv2013

A comparison of old and new definitions of the geometric measure of entanglement

Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review several known and new definitions, with the qualifying criterion being that for pure states the measure is a linear or logarithmic function of the maximal fidelity with product states. The entanglement axioms and properties of the measures are studied, and qualitative and quantitative comparisons are made between all definitions. Streltsov et al. [New J. Phys 12 123004 (2010)] proved the equivalence of two linear definitions of GM, whereas we show that the corresponding logarithmic definitions are distinct. Certain classes of states such as "maximally correlated states" and isotropic states are particularly valuable for this analysis. A little-known GM definition is found to be the first one to be both normalized and weakly monotonous, thus being a prime candidate for future studies of multipartite entanglement. We also find that a large class of graph states, which includes all cluster states, have a "universal" closest separable state that minimizes the quantum relative entropy, the Bures distance and the trace distance.

quant-ph↗
arXiv2013

Unextendible Product Basis for Fermionic Systems

We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an explicit example of generalized fermionic unextendible product basis (FUPB) of minimum cardinality $N(M-N)+1$ for any $N\ge2,M\ge4$. We also show that any bipartite antisymmetric space $\wedge^ 2 \bC^M$ of codimension two is spanned by Slater determinants, and the spaces of higher codimension may not be spanned by Slater determinants. Furthermore, we construct an example of complex FUPB of $N=2,M=4$ with minimum cardinality $5$. In contrast, we show that a real FUPB does not exist for $N=2,M=4$ . Finally we provide a systematic construction for FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.

quant-ph↗
arXiv2013

Dynamics of quantum discord in the purification process

We investigate the dynamics of quantum discord during the purification process. In the case of Werner states, it is shown that quantum discord is increased after a round of purification protocol. Furthermore, quantum mutual information and classical correlation is also increased during this process.Wealso give an analytic expression for a class of higher dimensional states which have additive quantum discord.

quant-ph↗
arXiv2013

On the optimality of approximation schemes for the classical scheduling problem

We consider the classical scheduling problem on parallel identical machines to minimize the makespan, and achieve the following results under the Exponential Time Hypothesis (ETH) 1. The scheduling problem on a constant number $m$ of identical machines, which is denoted as $Pm||C_{max}$, is known to admit a fully polynomial time approximation scheme (FPTAS) of running time $O(n) + (1/ε)^{O(m)}$ (indeed, the algorithm works for an even more general problem where machines are unrelated). We prove this algorithm is essentially the best possible in the sense that a $(1/ε)^{O(m^{1-δ})}+n^{O(1)}$ time FPTAS for any $δ>0$ implies that ETH fails. 2. The scheduling problem on an arbitrary number of identical machines, which is denoted as $P||C_{max}$, is known to admit a polynomial time approximation scheme (PTAS) of running time $2^{O(1/ε^2\log^3(1/ε))}+n^{O(1)}$. We prove this algorithm is nearly optimal in the sense that a $2^{O((1/ε)^{1-δ})}+n^{O(1)}$ time PTAS for any $δ>0$ implies that ETH fails, leaving a small room for improvement. To obtain these results we will provide two new reductions from 3SAT, one for $Pm||C_{max}$ and another for $P||C_{max}$. Indeed, the new reductions explore the structure of scheduling problems and can also lead to other interesting results. For example, using the framework of our reduction for $P||C_{max}$, Chen et al. (arXiv:1306.3727) is able to prove the APX-hardness of the scheduling problem in which the matrix of job processing times $P=(p_{ij})_{m\times n}$ is of rank 3, solving the open problem mentioned by Bhaskara et al. (SODA 2013).

cs.CC↗
arXiv2013

Four-qubit pure states as fermionic states

The embedding of the $n$-qubit space into the $n$-fermion space with $2n$ modes is a widely used method in studying various aspects of these systems. This simple mapping raises a crucial question: does the embedding preserve the entanglement structure? It is known that the answer is affirmative for $n=2$ and $n=3$. That is, under either local unitary (LU) operations or with respect to stochastic local operations and classical communication (SLOCC), there is a one-to-one correspondence between the 2- (or 3)-qubit orbits and the 2- (or 3)-fermion orbits with 4 (or 6) modes. However these results do not generalize as the mapping from the $n$-qubit orbits to the $n$-fermion orbits with $2n$ modes is no longer surjective for $n>3$. Here we consider the case of $n=4$. We show that surprisingly, the orbit mapping from qubits to fermions remains injective under SLOCC, and a similar result holds under LU for generic orbits. As a byproduct, we obtain a complete answer to the problem of SLOCC equivalence of pure 4-qubit states.

quant-ph↗
arXiv2013

Proof of the Gour-Wallach conjecture

The absolute value of the hyperdeterminant of four qubits is a useful measure of genuine entanglement. We prove a recent conjecture of Gour and Wallach describing the pure maximally entangled four-qubit states with respect to this measure.

quant-ph↗
arXiv2013

A note on scheduling with low rank processing times

We consider the classical minimum makespan scheduling problem, where the processing time of job $j$ on machine $i$ is $p_{ij}$, and the matrix $P=(p_{ij})_{m\times n}$ is of a low rank. It is proved in (Bhaskara et al., SODA 2013) that rank 7 scheduling is NP-hard to approximate to a factor of $3/2-ε$, and rank 4 scheduling is APX-hard (NP-hard to approximate within a factor of $1.03-ε$). We improve this result by showing that rank 4 scheduling is already NP-hard to approximate within a factor of $3/2-ε$, and meanwhile rank 3 scheduling is APX-hard.

cs.CC↗
arXiv2013

Dimensions, lengths and separability in finite-dimensional quantum systems

Many important sets of normalized states in a multipartite quantum system of finite dimension d, such as the set S of all separable states, are real semialgebraic sets. We compute dimensions of many such sets in several low-dimensional systems. By using dimension arguments, we show that there exist separable states which are not convex combinations of d or less pure product states. For instance, such states exist in bipartite M x N systems when (M-1)(N-1)>1. This solves an open problem proposed in [J. Mod. Opt. 47 (2000), 377-385]. We prove that there exist a separable state rho and a pure product state, whose mixture has smaller length than that of rho. We show that any real rho in S, which is invariant under all partial transpose operations, is a convex sum of real pure product states. In the case of the 2 x N system, the number r of product states can be taken to be r=rank(rho). We also show that the general multipartite separability problem can be reduced to the case of real states. Regarding the separability problem, we propose two conjectures describing S as a semialgebraic set, which may eventually lead to an analytic solution in some low-dimensional systems such as 2 x 4, 3 x 3 and 2 x 2 x 2.

quant-ph↗
arXiv2013

Universal Subspaces for Local Unitary Groups of Fermionic Systems

Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \ket{v_{i_1}\we v_{i_2}\we...\we v_{i_N}}$ with $i_1<... 3. If $M$ is even, the well known BCS states are not LU-equivalent to any single occupancy state. Our main result is that for N=3 and $M$ even there is a universal subspace $\cW\subseteq\cS$ spanned by $M(M-1)(M-5)/6$ states $e_{i_1,...,i_N}$. Moreover the number $M(M-1)(M-5)/6$ is minimal.

quant-ph↗
arXiv2013

Approximating the optimal competitive ratio for an ancient online scheduling problem

We consider the classical online scheduling problem P||C_{max} in which jobs are released over list and provide a nearly optimal online algorithm. More precisely, an online algorithm whose competitive ratio is at most (1+ε) times that of an optimal online algorithm could be achieved in polynomial time, where m, the number of machines, is a part of the input. It substantially improves upon the previous results by almost closing the gap between the currently best known lower bound of 1.88 (Rudin, Ph.D thesis, 2001) and the best known upper bound of 1.92 (Fleischer, Wahl, Journal of Scheduling, 2000). It has been known by folklore that an online problem could be viewed as a game between an adversary and the online player. Our approach extensively explores such a structure and builds up a completely new framework to show that, for the online over list scheduling problem, given any ε>0, there exists a uniform threshold K which is polynomial in m such that if the competitive ratio of an online algorithm is ρ<=2, then there exists a list of at most K jobs to enforce the online algorithm to achieve a competitive ratio of at least ρ-O(ε). Our approach is substantially different from that of Gunther et al. (Gunther et al., SODA 2013), in which an approximation scheme for online over time scheduling problems is given, where the number of machines is fixed. Our method could also be extended to several related online over list scheduling models.

cs.DS↗
arXiv2013

Properties and construction of extreme bipartite states having positive partial transpose

We consider a bipartite quantum system H_A x H_B with M=dim H_A and N=dim H_B. We study the set E of extreme points of the compact convex set of all states having positive partial transpose (PPT) and its subsets E_r={rho in E: rank rho=r}. Our main results pertain to the subsets E_r^{M,N} of E_r consisting of states whose reduced density operators have ranks M and N, respectively. The set E_1 is just the set of pure product states. It is known that E_r^{M,N} is empty for 1< r <= min(M,N) and for r=MN. We prove that also E_{MN-1}^{M,N} is empty. Leinaas, Myrheim and Sollid have conjectured that E_{M+N-2}^{M,N} is not empty for all M,N>2 and that E_r^{M,N} is empty for 1 3. We introduce the notion of "good" states, show that all pure states are good and give a simple description of the good separable states. For a good state rho in E_{M+N-2}^{M,N}, we prove that the range of rho contains no product vectors and that the partial transpose of rho has rank M+N-2 as well. In the special case M=3, we construct good 3 x N extreme states of rank N+1 for all N>3.

math-ph↗
arXiv2013

Separability problem for multipartite states of rank at most four

One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.

quant-ph↗
arXiv2012

Qubit-qudit states with positive partial transpose

We show that the length of a qubit-qutrit separable state is equal to the max(r,s), where r is the rank of the state and s is the rank of its partial transpose. We refer to the ordered pair (r,s) as the birank of this state. We also construct examples of qubit-qutrit separable states of any feasible birank (r,s). We determine the closure of the set of normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). The boundary of this set consists of all separable states of length at most four. We prove that the length of any qubit-qudit separable state of birank (d+1,d+1) is d+1. We also show that all qubit-qudit PPT entangled states of birank (d+1,d+1) can be built in a simple way from edge states. If V is a subspace of dimension k<d in the tensor product of C^2 and C^d such that V contains no product vectors, we show that the set of all product vectors in the orthogonal complement of V is a vector bundle of rank d-k over the projective line. Finally, we explicitly construct examples of qubit-qudit PPT states (both separable and entangled) of any feasible birank.

quant-ph↗