Lin Chen

Lin Chen
Beihang University (BUAA) | BUAA · School of Mathematics and Systems Science

PhD
I invite collaboration for proving the so-called km conjecture, see my paper J. Phys. A: Math. Theor. 51 145301 (2018).

About

182
Publications
10,690
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,819
Citations
Citations since 2017
114 Research Items
1233 Citations
2017201820192020202120222023050100150200250300
2017201820192020202120222023050100150200250300
2017201820192020202120222023050100150200250300
2017201820192020202120222023050100150200250300
Introduction
My research interests are entanglement theory, quantum information, and mathematical physics. See my publication for more details. My university homepage in both Chinese and English is http://math.buaa.edu.cn/szdw/azcck/fjs/cl.htm .
Additional affiliations
March 2015 - present
Beihang University (BUAA)
Position
  • Professor (Associate)
Description
  • office: room E703-5, main building (主楼), shahe campus; research field: theoretical problems in quantum information, say entanglement theory, MUB, maximally entangled states, tensor rank, etc.
January 2015 - March 2015
Chinese Academy of Sciences
Position
  • visitor
Description
  • quantum information and entanglement theory
January 2014 - December 2014
Singapore University of Technology and Design
Position
  • PostDoc Position
Description
  • quantum computing, quantum encryption
Education
September 2003 - June 2008
Zhejiang University
Field of study
  • theoretical physics
September 1999 - June 2003
Zhejiang University
Field of study
  • physics

Publications

Publications (182)
Preprint
Quantum gravity between masses can produce entangled states in thought experiments. We extend the experiments to tripartite case and construct states equivalent to Greenberger- Horne-Zeilinger states and W states under stochastic local operations and classical communication. The entanglement relates to the evolution phases induced by gravitational...
Preprint
Full-text available
Coherence, discord and geometric measure of entanglement are important tools for measuring physical resources. We compute them at every steps of the Grover's algorithm. We summarize these resources's patterns of change. These resources are getting smaller at the step oracle and are getting bigger or invariant at the step diffuser. This result is si...
Article
Full-text available
Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We investigate the inertia of bipartite EWs constructed by the partial transpose of NPT states. Furthermore, we find out most of the inertia of the partial transpose of the two-qutrit bipartite NPT states. As an application, we extend our results to high-dimensio...
Article
Full-text available
Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modified measure and the extended measure for bipartite states. We present the analytical formula for the pure states in terms of the modified measure and the mixed states of tw...
Preprint
Full-text available
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator valued measure (POVM). Two types of decision errors in a QHT would occur. In this paper we focus on the asymmetric setting of QHT, where the two types of decision errors are treated unequally. Instead of ado...
Article
Full-text available
Quantum nonlocality is associated with the local indistinguishability of orthogonal states. Unextendible product basis (UPB), a widely used tool in quantum information, exhibits nonlocality, which is the powerful resource for quantum information processing. In this work, we extend the definitions of nonlocality and genuine nonlocality from states t...
Article
Full-text available
The multipartite unitary gates are called genuine if they are not product unitary operators across any bipartition. We mainly investigate the classification of genuine multipartite unitary gates of Schmidt rank two, by focusing on the multiqubit scenario. For genuine multipartite (excluding bipartite) unitary gates of Schmidt rank two, there is an...
Article
Full-text available
The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of 2 × 2 × 4 and 2 × 2 × 2 × 4 UPBs of size eight by using the existing four-qubit and five-qubit UPBs. As an application, we construct novel families of multipartite positive-partial-transpose entangl...
Preprint
Full-text available
We propose protocols for controlled remote implementation of operations with convincing control power. Sharing a $(2N+1)$-partite graph state, $2N$ participants collaborate to prepare the stator and realize the operation $\otimes_{j=1}^N\exp{[i\alpha_j\sigma_{n_{O_j}}]}$ on $N$ unknown states for distributed systems $O_j$, with the permission of a...
Article
Full-text available
Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial‐transpose(PT)‐moments of two‐qubit states, and completely describe the whole region, composed of the second and third PT‐moment...
Preprint
The multipartite unitary gates are called genuine if they are not product unitary operators across any bipartition. We mainly investigate the classification of genuine multipartite unitary gates of Schmidt rank two, by focusing on the multiqubit scenario. For genuine multipartite (excluding bipartite) unitary gates of Schmidt rank two, there is an...
Article
Full-text available
Quantum cost is a key ingredient in evaluating the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of a d-dimensional dense coding protocol is equal to d+3 when transmitting the classical message (0,0) and d+4 when transmitting another classical message. It appears as linear growth with the dimension and thus...
Article
Full-text available
We study $k$ -uniform states in heterogeneous systems whose local dimensions are not all the same. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$ -uniform states, we present two constructions of 2-uniform states in heterogeneous systems. We also constru...
Article
Full-text available
Genuineness and distillability of entanglement play a key role in quantum information tasks, and they are easily disturbed by the noise. We construct a family of multipar-tite states without genuine entanglement and distillability sudden death across every bipartition, respectively. They are realized by establishing the noise as the multipartite hi...
Preprint
Full-text available
We propose the notion of faithful coherent states based on the fidelity-based coherence witness. The criterion for detecting faithful coherent states can be restricted to a subclass of fidelity-based criterion under unitary transformations for single and bipartite systems. We can realize these unitary transformations by using quantum gates and circ...
Preprint
Full-text available
Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We investigate the inertias of bipartite EWs constructed by the partial transpose of NPT states. Furthermore, we find out most of the inertias of the patial transpose of the two-qutrit bipartite NPT states. As an application, we extend our results to high dimensi...
Preprint
Full-text available
Quantifying entanglement is an important issue in quantum information theory. A straightforward method to quantify entanglement is to measure the distance between the entangled state and the separable sets under the fidelity, distance norm and so on. However, there are few results on the entanglement measure in terms of trace norm. Here we consider...
Preprint
Full-text available
The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing four-qubit and five-qubit UPBs. As an application, we construct novel families of multipartite positive-partia...
Preprint
Full-text available
The quantum cost is a key ingredient to evaluate the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of d-dimensional dense coding protocol is equal to d+3 when transmitting the classical message (0,0), and that is equal to d+4 when transmitting other classical message. It appears linear growth with the dimens...
Preprint
Full-text available
A set of multipartite orthogonal quantum states is strongly nonlocal if it is locally irreducible for every bipartition of the subsystems [Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four- and five-partite systems, the existence of strongly nonlocal sets in $N$-partite systems remains unknown when $N\geq 6...
Article
Full-text available
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving local measurement can be performed to this set. I...
Article
Full-text available
Characterizing the relations among the three bipartite reduced density operators ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> AB </sub> , ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> AC </sub> and ρ <sub xmlns:mml="http://www.w3.org/1998/Math/M...
Preprint
Full-text available
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to inves...
Article
Full-text available
It is conjectured that four mutually unbiased bases in dimension 6 do not exist in quantum information. The conjecture is equivalent to the nonexistence of some three 6×6 complex Hadamard matrices (CHMs) with Schmidt rank at least 3. We investigate the 6×6 CHM U of Schmidt rank 3 containing two nonintersecting identical 3×3 submatrices V, i.e. U=12...
Article
Full-text available
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to inves...
Article
Full-text available
Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points...
Preprint
Full-text available
Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points...
Preprint
Full-text available
The complete classification of $6\times 6$ complex Hadamard matrices (CHMs) is a long-standing open problem. In this paper we investigate a series of CHMs, such as the CHMs containing a $2\times 3$ submatrix with rank one, the CHMs containing exactly three distinct elements and all elements of the first row being one, the $H_2$-reducible matrices c...
Preprint
Full-text available
Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then the $H_2$-reducible matrix in the four MUBs has exactly nine $2\times2$ Hadamard submatrices. We apply our result to exclude from the four MUBs some known CHMs, such as s...
Preprint
Full-text available
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition. Most known constructions of strongly nonlocal orthogonal product set (OPS) are limited to tripartite systems, and they are lack of intuitive structures. In this work, based on the decomposition for the outermost layer of an $n$-di...
Article
Full-text available
Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then the H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepac...
Preprint
Full-text available
Unextendible product basis (UPB), a widely used tool in quantum information, exhibits nonlocality which is the powerful resource for quantum information processing. In this work we extend the definitions of nonlocality and genuine nonlocality from states to operators. We also extend UPB to the notions of unextendible product operator basis, unexten...
Article
Full-text available
It is impossible to mask an arbitrary quantum state into the correlations between two subsystems such that the original information is completely unknown to each local system. This is the no-masking theorem proposed by Modi et al. [K. Modi, A. K. Pati, A. Sen(De), and U. Sen, Phys. Rev. Lett. 120, 230501 (2018)]. In this work, we propose the concep...
Article
Full-text available
The monogamy of entanglement means that entanglement cannot be freely shared. In 2014, Oliveira et al. [T. R. de Oliveira, M. F. Cornelio, and F. F. Fanchini, Phys. Rev. A 89, 034303 (2014)] proposed a monogamy relation in the linear version and considered it in terms of entanglement of formation. Here we generalize the above version and consider a...
Article
Full-text available
The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the proof of Theorem 20 in our work [L. Qian et al., Phys. Rev. A 99, 032312 (2019)], and presented a sufficient and necessary condition for the separability of completely symmetric (CS) states in the two-qutrit system. While being technically correct, the p...
Article
Full-text available
Characterizing the zero entries in multipartite unitary matrices plays an important role in evaluating the usefulness of such matrices in quantum information. We investigate the zero entries in unitary and product unitary matrices. On one hand, we study the quantity properties of the zero entries in the multiqubit and bipartite product unitary matr...
Article
Full-text available
A multipartite state that is not the convex sum of bipartite product states is said to be a genuine multipartite entangled (GME) state, which offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on uncertainty relations for chosen observables of subsys...
Preprint
Full-text available
Multipartite quantum system is complex. Characterizing the relations among the three bipartite reduced density operators $\rho_{AB}$, $\rho_{AC}$ and $\rho_{BC}$ of a tripartite state $\rho_{ABC}$ has been an open problem in quantum information. One of such relations has been reduced by [Cadney et al, LAA. 452, 153, 2014] to a conjectured inequalit...
Preprint
Full-text available
We propose entanglement criteria for multipartite systems via symmetric informationally complete (SIC) measurement and general symmetric informationally complete (GSIC) measurement. We apply these criteria to detect entanglement of multipartite states, such as the convex of Bell states, entangled states mixed with white noise. It is shown that thes...
Article
Full-text available
The distillability conjecture of two-copy 4×4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times 4$$\end{document} Werner states is one of the main open problems in...
Preprint
Full-text available
Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we present a lower and upper bound of a type II error of the hypothesis testing. Next we present a lower bound of the s...
Article
Full-text available
It is known that every two-qubit unitary operation has Schmidt rank one, two or four, and the construction of three-qubit unitary gates in terms of Schmidt rank remains an open problem. We explicitly construct the gates of Schmidt rank from one to seven. It turns out that the three-qubit Toffoli and Fredkin gate, respectively, have Schmidt rank two...
Article
Full-text available
Absolutely maximally entangled (AME) states are closely related to quantum error correction codes. They are typically defined in homogeneous systems. However, the heterogeneous system is very common in a practical setup. In this work, we focus on the AME states in tripartite heterogeneous systems. We first introduce irreducible AME states as the ba...
Article
Full-text available
To quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement measure is entanglement monotone and convex are presented, as well as the interpretation of smoothed one‐shot entanglement cost. Next, a difference between...
Preprint
Full-text available
An important problem in quantum information is to construct multiqubit unextendible product bases (UPBs). By using the unextendible orthogonal matrices, we construct a 7-qubit UPB of size 11. It solves an open problem in [Quantum Information Processing 19:185 (2020)]. Next, we graph-theoretically show that the UPB is locally indistinguishable in th...
Preprint
Full-text available
Genuine multipartite entanglement (GME) offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on local sum uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy $n$-partite W state when...
Preprint
Full-text available
Genuineness and distillability of entanglement play a key role in quantum information tasks, and they are easily disturbed by the noise. We construct a family of multipartite states without genuine entanglement and distillability sudden death across every bipartition, respectively. They are realized by establishing the noise as the multipartite hig...
Article
Full-text available
The pure entangled state is of vital importance in the field of quantum information. The process of asymptotically extracting pure entangled states from many copies of mixed states via local operations and classical communication is called entanglement distillation. The entanglement distillability problem, which is a long-standing open problem, ask...
Preprint
Full-text available
A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving measurement can be performed to this set. In gene...
Article
Full-text available
Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We study the inertias of EWs, i.e., the triplet of the numbers of negative, zero, and positive eigenvalues respectively. We focus on the EWs constructed by the partial transposition of states with non-positive partial trans- poses. We provide a method to generate...
Article
Full-text available
There are practical motivations to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. Here, the case that the states are two‐qubit Werner states is considered. The intervals of parameters of two‐qubit Werner states are revealed such that the tripartite state is genuinely entangled. Furthermo...
Article
Full-text available
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor prod- uct of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled (GE) state when the range of both bipartite states are entanglement-breakin...
Article
Full-text available
We provide several bounds on the maximum size of MU k-Schmidt bases in Cd⊗Cd′. We first give some upper bounds on the maximum size of MU k-Schmidt bases in Cd⊗Cd′ by conversation law. Then we construct two maximally entangled mutually unbiased (MU) bases in the space C2⊗C3, which is the first example of maximally entangled MU bases in Cd⊗Cd′ when d...
Article
Full-text available
Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existence results for sets of strongly nonlocal orthogonal states are limited to product states. In this paper, based on the Rubik's cube, we give the first const...
Preprint
Full-text available
A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed. Based on the connections among $k$-uniform states, orthogonal arrays and linear codes, we give general constructions for $k$-uniform states. We show that when $d\geq 4k-2$ (resp. $d\geq 2k-1$) is a prime power...
Article
Full-text available
Preparing the locally maximally mixed (LMM) states is a physically operational work. We investigate the set \(\mathcal{P}_d\) containing two-qudit LMM states. We show that the point with a canonical decomposition (CD) has either the unique or infinitely many CDs. Next we show that the point in \(\mathcal{P}_2\) has infinitely many CDs. Further we c...
Preprint
Full-text available
To quantify the entanglement is one of the most important topics in quantum entanglement theory. In [arXiv: 2006.12408], the authors proposed a method to build a measure from the orginal domain to a larger one. Here we apply that method to build an entanglement measure from measures for pure states. First, we present conditions when the entanglemen...
Preprint
Full-text available
Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We study the matrix inertias of EWs with a focus on the EWs constructed by the partial transposition of states with non-positive partial transposes. We provide a method to generate more inertias from a given inertia by the relevance between inertias. Based on tha...
Preprint
Full-text available
Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existence results for sets of strongly nonlocal orthogonal states are limited to product states. In this paper, based on the Rubik's cube, we give the first const...
Preprint
Full-text available
It is known that every two-qubit unitary operation has Schmidt rank one, two or four, and the construction of three-qubit unitary gates in terms of Schmidt rank remains an open problem. We explicitly construct the gates of Schmidt rank from one to seven. It turns out that the three-qubit Toffoli and Fredkin gate respectively have Schmidt rank two a...
Article
Full-text available
We completely characterize the condition when a tile structure provides an unextendible product basis (UPB) and construct UPBs of different large sizes in Cm⊗Cn. In particular, we show that there exists a UPB of size (mn−4⌊m−12⌋) in Cm⊗Cn for any n≥m≥3, which solves an open problem [S. Halder et al., Phys. Rev. A 99, 062329 (2019)]. As an applicati...
Preprint
Full-text available
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subsp...
Preprint
Full-text available
We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$-uniform states, we present two constructions of $2$-uniform states in heterogeneous systems. We also construct a family of...
Article
Full-text available
The construction of multiqubit unextendible product bases (UPBs) is an important problem in quantum information. We construct a 7-qubit UPB of size 10 by studying the unextendible orthogonal matrices. We apply our result to construct an 8-qubit UPB of size 18. Our results solve an open problem proposed in (J Phys A 51:265302, 2018). We also investi...
Article
Full-text available
We investigate the number of zero entries in a unitary matrix. We show that the sets of numbers of zero entries for n×n unitary and orthogonal matrices are the same. They are both the set {0,1,…,n2−n−4,n2−n−2,n2−n} for n>4. We explicitly construct examples of orthogonal matrices with the numbers in the set. We apply our results to construct a neces...
Article
Full-text available
Recently, there has been increasing interest in designing schemes for quantum computations that are robust against errors. Although considerable research has been devoted to quantum error correction schemes, much less attention has been paid to optimizing the speed it takes to perform a quantum computation and developing computation models that act...
Preprint
Full-text available
It is an interesting problem to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. We consider the case that the states are two-qubit Werner states, we construct the interval of parameter of Werner states such that the tripartite state is genuine entangled. Further, we present the way of det...
Article
Full-text available
In this article, we consider the monogamy relations for the generalized W-class states. Here we first present an analytical formula on Tsallis-q entanglement (TqEE) and Tsallis-q entanglement of assistance (TqEEoA) of a reduced density matrix for a generalized W-class state. By using the analytical formula, we present a monogamy relation in terms o...
Preprint
Full-text available
We construct the notions of tile and U-tile structures. A tile structure corresponds to an $m\times n$ unextendible product basis (UPB) if and only if it is a U-tile structure. We construct UPBs of large size in terms of the U-tile structures. In particular we solve an open problem in [S. Halder et al., Phys. Rev. A 99, 062329 (2019)]. As an applic...
Article
Full-text available
Symmetry is one of the central mysteries of quantum mechanics and plays an essential role in multipartite entanglement. In this paper, we consider the separability problem of quantum states in the symmetric space. We establish the relation between the separability of multiqubit symmetric states and the decomposability of Hermitian positive semidefi...
Article
Full-text available
Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank three. The CHM is equivalent to a controlled unitary operation on the qubit-qutrit system via local unitary tran...
Preprint
Full-text available
Absolutely maximally entangled (AME) states are typically defined in homogeneous systems. However, the quantum system is more likely to be heterogeneous in a practical setup. Therefore, in this work we pay attention to the construction of AME states in tripartite heterogeneous systems. We completely determine the existence of tripartite AME states...
Article
Full-text available
We investigate the number of real entries of an n×n complex Hadamard matrix. We analytically derive the numbers when n = 2, 3, 4, 6. In particular, the number can be any one of 0–22, 24, 25, 26, 30 for n = 6. We apply our result to the existence of four mutually unbiased bases in dimension six, which is a long-standing open problem in quantum physi...
Preprint
Full-text available
We construct two mutually unbiased bases by maximally entangled states (MUMEB$s$) in $\mathbb{C}^{2}\otimes \mathbb{C}^{3}$. This is the first example of MUMEB$s$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d'}$ when $d\nmid d'$, namely $d'$ is not divisible by $d$. We show that they cannot be extended to four MUBs in $\mathbb{C}^6$. We propose a recursi...