Physical Review A

Detecting k -nonseparability via quantum Fisher information

Yan Hong, Shunlong Luo, Hongting Song

Published Apr 10, 2015• 34 citations

Abstract

The $k$-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of $k$-nonseparability of $n$-partite quantum states from an information perspective and obtain some $k$-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many $k$-nonseparable states, and their advantages over an important and well-known $k$-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.

DOI: 10.1103/physreva.91.042313

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Physical Review A

Detecting k -nonseparability via quantum Fisher information

Yan Hong, Shunlong Luo, Hongting Song

Published Apr 10, 2015• 34 citations

Publisher

Abstract

The

k

-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of

k

-nonseparability of

n

-partite quantum states from an information perspective and obtain some

k

-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many

k

-nonseparable states, and their advantages over an important and well-known

k

-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.

DOI: 10.1103/physreva.91.042313

Related papers

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Yan Hong, Xianfei Qi, Ting Gao +1 more

In this paper, we focus on two different kinds of multipartite correlation, k -nonseparability and k -partite entanglement, both of which can describe the essential characteristics of multipartite entanglement. We propose effective methods to detect k -nonseparability and k -partite entanglement in terms of quantum Fisher information. We illustrate the significance of our results and show that they identify some k -nonseparability and k -partite entanglement that cannot be identified by known criteria by several concrete examples.In this paper, we focus on two different kinds of multipartite correlation, k -nonseparability and k -partite entanglement, both of which can describe the essential characteristics of multipartite entanglement. We propose effective methods to detect k -nonseparability and k -partite entanglement in terms of quantum Fisher information. We illustrate the significance of our results and show that they identify some k -nonseparability and k -partite entanglement that cannot be identified by known criteria by several concrete examples.

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We investigate $k$ -nonseparability of $n$ -partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some $k$ -nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of $k$ -nonseparability through several examples.We investigate $k$-nonseparability of $n$-partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some $k$-nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of $k$-nonseparability through several examples.

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The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate $k$ -nonseparability and $k$ -partite entanglement of $N$ -partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$ .[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its $k$ -nonseparability or $k$ -partite entanglement,so these inequalities present the hierarchic classifications of $k$ -nonseparability or $k$ -partite entanglement for all $N$ -partite quantum states from $N$ -nonseparability to $2$ -nonseparability or from $2$ -partite entanglement to $N$ -partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some $k$ -nonseparability and $k$ -partite entanglement that remain undetected by other methods,and these are illustrated through some examples.The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$.[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its $k$-nonseparability or $k$-partite entanglement,so these inequalities present the hierarchic classifications of $k$-nonseparability or $k$-partite entanglement for all $N$-partite quantum states from $N$-nonseparability to $2$-nonseparability or from $2$-partite entanglement to $N$-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods,and these are illustrated through some examples.

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Detection of $k$ -nonseparable $n$ -partite quantum statesDetection of $k$-nonseparable $n$-partite quantum states

Ting Gao, Yan Hong

The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$ -separability criteria of mixed $n$ -partite ( $n\geq 3$ ) quantum states to detect $k$ -nonseparable $n$ -partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.

arXiv:1207.1596Jul 6, 20120 citations

The

k

-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of

k

-nonseparability of

n

-partite quantum states from an information perspective and obtain some

k

-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many

k

-nonseparable states, and their advantages over an important and well-known

k

-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.

We investigate

k

-nonseparability of

n

-partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some

k

-nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of

k

-nonseparability through several examples.

The

k

-separability of mixed

n

-partite (

n\geq 3

) quantum states is mainly discussed in this paper. We obtain practical

k

-separability criteria to identify

k

-nonseparable mixed multipartite states in arbitrary dimensional quantum systems and detect genuine

n

-partite entanglement (

k=2

) and entanglement (

k=3

) which have previously not been identified. No optimization or eigenvalue evaluation is needed, our criteria can be evaluated by simple computations involving components of the density matrix and can be implemented in today's experiments.

The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate

k

-nonseparability and

k

-partite entanglement of

N

-partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang

et

al

.[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its

k

-nonseparability or

k

-partite entanglement,so these inequalities present the hierarchic classifications of

k

-nonseparability or

k

-partite entanglement for all

N

-partite quantum states from

N

-nonseparability to

2

-nonseparability or from

2

-partite entanglement to

N

-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some

k

-nonseparability and

k

-partite entanglement that remain undetected by other methods,and these are illustrated through some examples.

Detection of

k

-nonseparable

n

-partite quantum states

The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful

k

-separability criteria of mixed

n

-partite (

n\geq 3

) quantum states to detect

k

-nonseparable

n

-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.