Quantum Information and Computation

Indecomposability of entanglement witnesses

Xiaofei Qi, Jinchuan Hou

Published Apr 1, 2015• 4 citations

Abstract

We present a way to construct indecomposable entanglement witnesses from any permutations pi with pi^2 not equal to id for any finite dimensional bipartite systems. Some new bounded entangled states are also found, which can be detected by such witnesses while cannot be distinguished by PPT criterion, realignment criterion, etc.

DOI: 10.26421/qic15.5-6-7

Related papers

Indecomposability of entanglement witnesses constructed from any permutations

QiXiao-Fei, HouJin-Chuan

We present a way to construct indecomposable entanglement witnesses from any permutations π with π2 ≠ id for any finite dimensional bipartite systems. Some new bounded entangled states are also fou...

Quantum Information and ComputationApr 1, 20150 citations

Constructing entanglement witnesses for infinite-dimensional systems

Jinchuan Hou, Xiaofei Qi

arXiv:1005.5530Physical Review AJun 30, 201035 citations

How to construct indecomposable entanglement witnesses

Dariusz Chruściński, Andrzej Kossakowski

We present a very simple method for constructing indecomposable entanglement witnesses out of a given pair—an entanglement witness W and the corresponding state detected by W . This method may be used to produce new classes of atomic witnesses which are able to detect the 'weakest' quantum entanglement. Actually, it works perfectly in the multipartite case, too. Moreover, this method provides a powerful tool for constructing new examples of bound entangled states.

arXiv:0712.1114Journal of Physics A Mathematical and TheoreticalMar 26, 200837 citations

Positive finite rank elementary operators and characterizing entanglement of states

Xiaofei Qi, Jinchuan Hou

In this paper, some indecomposable positive finite rank elementary operators of order ( n , n ) are constructed. This allows us to give a simple necessary and sufficient criterion for the separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order (2, 2) and obtain some new mixed entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

arXiv:1008.3682Journal of Physics A Mathematical and TheoreticalMay 3, 201134 citations

Indecomposability of entanglement witnesses constructed from any permutations

Xiaofei Qi, Jinchuan Hou

arXiv:1406.4954Jun 19, 20140 citations

Entanglement detection beyond the computable cross-norm or realignment criterion

Chengjie Zhang, Yong-Sheng Zhang, Shun Zhang +1 more

arXiv:0709.3766Physical Review AJun 2, 200893 citations

Quantum Information and Computation

Indecomposability of entanglement witnesses

Xiaofei Qi, Jinchuan Hou

Published Apr 1, 2015• 4 citations

Publisher

Abstract

DOI: 10.26421/qic15.5-6-7

Related papers

Indecomposability of entanglement witnesses constructed from any permutations

QiXiao-Fei, HouJin-Chuan

Quantum Information and ComputationApr 1, 20150 citations

Constructing entanglement witnesses for infinite-dimensional systems

Jinchuan Hou, Xiaofei Qi

It is shown that every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\ensuremath{\alpha}I+T$ with $\ensuremath{\alpha}$ a non-negative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing an entanglement witness and apply them to obtain some entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.It is shown that every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\ensuremath{\alpha}I+T$ with $\ensuremath{\alpha}$ a non-negative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing an entanglement witness and apply them to obtain some entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

arXiv:1005.5530Physical Review AJun 30, 201035 citations

How to construct indecomposable entanglement witnesses

Dariusz Chruściński, Andrzej Kossakowski

arXiv:0712.1114Journal of Physics A Mathematical and TheoreticalMar 26, 200837 citations

Positive finite rank elementary operators and characterizing entanglement of states

Xiaofei Qi, Jinchuan Hou

arXiv:1008.3682Journal of Physics A Mathematical and TheoreticalMay 3, 201134 citations

Indecomposability of entanglement witnesses constructed from any permutations

Xiaofei Qi, Jinchuan Hou

Let $n\geq 2$ and $Φ_{n,t,π}: M_n({\mathbb C}) \rightarrow M_n({\mathbb C})$ be a linear map defined by $Φ_{n,t,π}(A)=(n-t)\sum_{i=1}^nE_{ii}AE_{ii}+t\sum_{i=1}^nE_{i,π(i)}AE_{i,π(i)}^†-A$ , where $0\leq t\leq n$ , $E_{ij}$ s are the matrix units and $π$ is a non-identity permutation of $(1,2,\cdots,n)$ . Denote by $\{{ F}_s: s=1,2\ldots, k\}$ the set of all minimal cycles of $π$ and $l(π)=\max\{\# { F}_s: s=1,2,\ldots,k\}$ the length of $π$ . It is shown that the Hermitian matrix $W_{n,t,π}$ induced by $Φ_{n,t,π}$ is an indecomposable entanglement witness if and only if $π^2\not={\rm id}$ (the identity permutation) and $0Let $n\geq 2$ and $Φ_{n,t,π}: M_n({\mathbb C}) \rightarrow M_n({\mathbb C})$ be a linear map defined by $Φ_{n,t,π}(A)=(n-t)\sum_{i=1}^nE_{ii}AE_{ii}+t\sum_{i=1}^nE_{i,π(i)}AE_{i,π(i)}^†-A$, where $0\leq t\leq n$, $E_{ij}$s are the matrix units and $π$ is a non-identity permutation of $(1,2,\cdots,n)$. Denote by $\{{ F}_s: s=1,2\ldots, k\}$ the set of all minimal cycles of $π$ and $l(π)=\max\{\# { F}_s: s=1,2,\ldots,k\}$ the length of $π$. It is shown that the Hermitian matrix $W_{n,t,π}$ induced by $Φ_{n,t,π}$ is an indecomposable entanglement witness if and only if $π^2\not={\rm id}$ (the identity permutation) and $0

arXiv:1406.4954Jun 19, 20140 citations

Entanglement detection beyond the computable cross-norm or realignment criterion

Chengjie Zhang, Yong-Sheng Zhang, Shun Zhang +1 more

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the criterion based on Bloch representations, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analog of permutation separability criteria in the even-partite systems.Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the criterion based on Bloch representations, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analog of permutation separability criteria in the even-partite systems.

arXiv:0709.3766Physical Review AJun 2, 200893 citations

T

a finite rank self-adjoint operator. We also provide two methods of constructing an entanglement witness and apply them to obtain some entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

Let

n\geq 2

and

Φ_{n,t,π}: M_n({\mathbb C}) \rightarrow M_n({\mathbb C})

be a linear map defined by

Φ_{n,t,π}(A)=(n-t)\sum_{i=1}^nE_{ii}AE_{ii}+t\sum_{i=1}^nE_{i,π(i)}AE_{i,π(i)}^†-A

, where

0\leq t\leq n

E_{ij}

s are the matrix units and

π

is a non-identity permutation of

(1,2,\cdots,n)

. Denote by

\{{ F}_s: s=1,2\ldots, k\}

the set of all minimal cycles of

π

and

l(π)=\max\{\# { F}_s: s=1,2,\ldots,k\}

the length of

π

. It is shown that the Hermitian matrix

W_{n,t,π}

induced by

Φ_{n,t,π}

is an indecomposable entanglement witness if and only if

π^2\not={\rm id}

(the identity permutation) and $0