Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

The full separability of three-qubit superposition state and its decayed states in white noise environment

Weidong Shen, Xiaoyu Chen

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Abstract The research on the separability of quantum states is one of the important research directions in quantum information theory. In this paper, we propose a new entanglement witness to study the full separability of the superposition of three-qubit W and <?CDATA $\bar{{\rm{W}}}$?> W ¯ (the qubit inverted W state) states in white noise environment. The witness accounts for most results of separable condition of the state obtained with numerical calculation. The witness also accounts for the decayed state which is the superposition state with and terms decayed by a factor. The separability criterion from our witness is better than that of the further generalized Wootters formula.

DOI
10.1088/1742-6596/1738/1/012087

Related papers

Entanglement properties of GHZ and W superposition state and its decayed states*

Xin-Feng Jin, Li-zhen Jiang, Xiaoyu Chen

We use the generalized Wootters formula, the positive partial transpose (PPT) criterion and the matched entanglement witness, to detect entanglement of three-qubit GHZ and W superposition state and its decayed states. It shows that the results of the generalized Wootters formula in the part near the W state are tight. In the other parts, the PPT criterion is superior to the generalized Wootters formula. Furthermore, we investigate the relationship between entanglement and coherence.

Chinese Physics B•Dec 30, 2020•2 citations

New entanglement Witnesses and Bell Operator for n-qubits related to Hilbert-Schmidt decompositions

Y. Ben-Aryeh, A. Mann

The use of entanglement witness (EW) for non-full separability and the Bell operator for non-local hidden-variables (LHV) model are analyzed by relating them to the Hilbert-Schmidt (HS) decomposition of n-qubits states and these methods are applied explicitly to some 3 and 4 qubits states. EW for non-full separability (fs) is given by fs parameter minus operator G where the choice of G in the HS decomposition leads to the fs parameter and to the condition for non-separability by using criterions which are different from those used for genuine entanglement. We analyze especially entangled states with probability p mixed with white noise with probability 1-p and find the critical value p(crit.) above which the system is not fully separable. As the choice of EW might not be optimal we add to the analysis of EW explicit construction of fully separable density matrix and find the critical value p below which the system is fully separable. If the two values for p coincide we conclude that this parameter gives the optimal result. Such optimal results are obtained in the present work for some 3 and 4 qubits entangled states mixed with white noise. The use of partial-transpose (PT ) (say relative to qubit A) gives also p value above which the system is not fully separable. The use of EW gives better results (or at least equal) than those obtained by PT .

•May 26, 2019•0 citations

Entanglement witnesses of four-qubit tripartite separable quantum states*

Miao Xu, Weifeng Zhou, Feng Chen +2 more

Abstract A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.

Communications in Theoretical Physics•Dec 7, 2021•0 citations

Noise tolerance of Dicke states

Xiaoyu Chen, Li-zhen Jiang

Starting from explicitly constructing an entanglement witness for the mixture of a Dicke state with white noise (noisy Dicke state), we provide an entanglement criterion for any multiqubit state. The criterion is necessary and sufficient for noisy $W$ states of three, four, and five qubits. We demonstrate an entanglement criterion for any four-qubit state. The criterion is necessary and sufficient for the generalized noisy four-qubit Dicke states. We present the sufficient criterion of full separability for a noisy $2k$ qubit Dicke state with $k$ excitations. Then we generalize the entanglement witness and criterion to the mixture of white noise and generic $n$-qubit Dicke state with $k$ excitations based on strong numeric evidence. Apart from noisy Dicke states, we also consider the entanglement properties of simultaneously amplitude damped and dephased Dicke states, and depolarized multiqubit $W$ states.

Physical Review A•Jan 9, 2020•20 citations

A Necessary and Sufficient Entanglement Criterion of N-qubit System Based on Correlation Tensor

Fenglin Wu, Siyuan Liu, Wen‐Li Yang +2 more

Great advances have been achieved in studying characteristics of entanglement for fundamentals of quantum mechanics and quantum information processing. However, even for N-qubit systems, the problem of entanglement criterion has not been well solved. In this Letter, using the method of state decomposition and high order singular value decomposition (HOSVD), we propose a necessary and sufficient entanglement criterion for general N-qubit systems. As an example, we apply our method to study the multi-qubit W state with white noise. We not only obtain the separability critical point, which is tight and thus better than known results, but also the separate states ensemble for decomposition. More examples are presented to show our criterion is accurate, which is tighter than the well-known positive partial transpose criterion. For two-qubit case, we can provide an entanglement measurer which gives similar results with concurrence up to a factor. Our results pave the way to solve the entanglement-separability criterion for more general cases.

arXiv:2205.05323•May 11, 2022•0 citations

Necessary and sufficient criterion for k-separability of N-qubit noisy GHZ states

Xiaoyu Chen, Li-zhen Jiang, Zhu‐An Xu

A Multipartite entangled state has many different kinds of entanglements specified by the number of partitions. The most essential example of multipartite entanglement is the entanglement of multi-qubit Greenberger–Horne–Zeilinger (GHZ) state in white noise. We explicitly construct the entanglement witnesses for these states with stabilizer generators of the GHZ states. For an [Formula: see text] qubit GHZ state in white noise, we demonstrate the necessary and sufficient criterion of separability when it is divided into [Formula: see text] parties with [Formula: see text] for arbitrary [Formula: see text] and [Formula: see text]. The criterion covers more than a half of all kinds of partial entanglements for [Formula: see text]-qubit GHZ states in white noise. For the rest of multipartite entanglement problems, we present a method to obtain the sufficient conditions of separability. As an application, we consider [Formula: see text] qubit GHZ state as a codeword of the degenerate quantum code passing through depolarizing channel. We find that the output state is neither genuinely entangled nor fully separable when the quantum channel capacity reduces from positive to zero.

arXiv:1605.08496•International Journal of Quantum Information•Jun 1, 2018•10 citations
Abstract The research on the separability of quantum states is one of the important research directions in quantum information theory. In this paper, we propose a new entanglement witness to study the full separability of the superposition of three-qubit W and <?CDATA $\bar{{\rm{W}}}$?> W ¯ (the qubit inverted W state) states in white noise environment. The witness accounts for most results of separable condition of the state obtained with numerical calculation. The witness also accounts for the decayed state which is the superposition state with and terms decayed by a factor. The separability criterion from our witness is better than that of the further generalized Wootters formula.
The use of entanglement witness (EW) for non-full separability and the Bell operator for non-local hidden-variables (LHV) model are analyzed by relating them to the Hilbert-Schmidt (HS) decomposition of n-qubits states and these methods are applied explicitly to some 3 and 4 qubits states. EW for non-full separability (fs) is given by fs parameter minus operator G where the choice of G in the HS decomposition leads to the fs parameter and to the condition for non-separability by using criterions which are different from those used for genuine entanglement. We analyze especially entangled states with probability p mixed with white noise with probability 1-p and find the critical value p(crit.) above which the system is not fully separable. As the choice of EW might not be optimal we add to the analysis of EW explicit construction of fully separable density matrix and find the critical value p below which the system is fully separable. If the two values for p coincide we conclude that this parameter gives the optimal result. Such optimal results are obtained in the present work for some 3 and 4 qubits entangled states mixed with white noise. The use of partial-transpose (PT ) (say relative to qubit A) gives also p value above which the system is not fully separable. The use of EW gives better results (or at least equal) than those obtained by PT .
Abstract A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.
Starting from explicitly constructing an entanglement witness for the mixture of a Dicke state with white noise (noisy Dicke state), we provide an entanglement criterion for any multiqubit state. The criterion is necessary and sufficient for noisy WWW states of three, four, and five qubits. We demonstrate an entanglement criterion for any four-qubit state. The criterion is necessary and sufficient for the generalized noisy four-qubit Dicke states. We present the sufficient criterion of full separability for a noisy 2k2k2k qubit Dicke state with kkk excitations. Then we generalize the entanglement witness and criterion to the mixture of white noise and generic nnn-qubit Dicke state with kkk excitations based on strong numeric evidence. Apart from noisy Dicke states, we also consider the entanglement properties of simultaneously amplitude damped and dephased Dicke states, and depolarized multiqubit WWW states.
Great advances have been achieved in studying characteristics of entanglement for fundamentals of quantum mechanics and quantum information processing. However, even for N-qubit systems, the problem of entanglement criterion has not been well solved. In this Letter, using the method of state decomposition and high order singular value decomposition (HOSVD), we propose a necessary and sufficient entanglement criterion for general N-qubit systems. As an example, we apply our method to study the multi-qubit W state with white noise. We not only obtain the separability critical point, which is tight and thus better than known results, but also the separate states ensemble for decomposition. More examples are presented to show our criterion is accurate, which is tighter than the well-known positive partial transpose criterion. For two-qubit case, we can provide an entanglement measurer which gives similar results with concurrence up to a factor. Our results pave the way to solve the entanglement-separability criterion for more general cases.
A Multipartite entangled state has many different kinds of entanglements specified by the number of partitions. The most essential example of multipartite entanglement is the entanglement of multi-qubit Greenberger–Horne–Zeilinger (GHZ) state in white noise. We explicitly construct the entanglement witnesses for these states with stabilizer generators of the GHZ states. For an [Formula: see text] qubit GHZ state in white noise, we demonstrate the necessary and sufficient criterion of separability when it is divided into [Formula: see text] parties with [Formula: see text] for arbitrary [Formula: see text] and [Formula: see text]. The criterion covers more than a half of all kinds of partial entanglements for [Formula: see text]-qubit GHZ states in white noise. For the rest of multipartite entanglement problems, we present a method to obtain the sufficient conditions of separability. As an application, we consider [Formula: see text] qubit GHZ state as a codeword of the degenerate quantum code passing through depolarizing channel. We find that the output state is neither genuinely entangled nor fully separable when the quantum channel capacity reduces from positive to zero.