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

arXiv:quant-ph/0109102 · Physical Review A

Robustness of multiparty entanglement

Christoph Simon, Julia Kempe

Published May 9, 2002• 168 citations
arXivHTMLPDF

Abstract

We study the robustness of multiparty entanglement under local decoherence, modeled by partially depolarizing channels acting independently on each subsystem. Surprisingly, we find that the robustness of (GHZ) entanglement increases with the number of qubits. An n-qubit Greenberger-Horne-Zeilinger (GHZ) state can stand more than 55% local depolarization in the limit $\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}.$ GHZ states are more robust than other generic states of three and four qubits. We also study spin-squeezed states in the limit $\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}$ and find that they too can stand considerable local depolarization.

DOI
10.1103/physreva.65.052327

Related papers

Robustness of multiparty nonlocality to local decoherence

Sung Soon Jang, Yong Wook Cheong, Jaewan Kim +1 more

We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystem. To be specific, we consider an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state under a depolarization, dephasing, or dissipation channel, and examine nonlocality by testing violation of the Mermin-Klyshko inequality, which is one of Bell's inequalities for multiqubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an $N$-qubit GHZ state with even $N$ is extremely persistent against dephasing.

arXiv:quant-ph/0608236•Physical Review A•Dec 27, 2006•16 citations

Robustness of multiqubit entanglement in the independent decoherence model

Somshubhro Bandyopadhyay, Daniel A. Lidar

We study the robustness of the Greenberger-Horne-Zeilinger (``cat'') class of multipartite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of $N$-party entanglement is studied in the large $N$ limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes large and (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.

arXiv:quant-ph/0408174•Physical Review A•Oct 31, 2005•38 citations

Robustness of highly entangled multiqubit states under decoherence

Antoni Borràs, A. P. Majtey, Angel Ricardo Plastino +2 more

We investigate the decay of entanglement, due to decoherence, of multiqubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness-optimization problem that only involves states equivalent, under local unitary transformations, to the Greenberger-Horne-Zeilinger $|\text{GHZ}⟩$ state.

arXiv:0806.0779•Physical Review A•Feb 9, 2009•67 citations

MultiqubitWstates lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states

Aditi Sen, Ujjwal Sen, Marcin Wieśniak +2 more

The N-qubit states of the W class, for $N>10,$ lead to more robust (against noise admixture) violations of local realism, than the Greenberger-Horne-Zeilinger (GHZ) states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining $N\ensuremath{-}2$ qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.

arXiv:quant-ph/0211023•Physical Review A•Dec 9, 2003•116 citations

Robustness of multipartite entanglement under collisional decoherence

Yee‐Chia Yeo

The collision model of Ziman et al. was considered and the robustness of N -qubit Greenberger-Horne-Zeilinger (GHZ), W, and linear cluster states were studied. Our results show that N -qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of W states could be more robust than of linear cluster states.

Optics and Spectroscopy•Aug 1, 2007•3 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
We study the robustness of multiparty entanglement under local decoherence, modeled by partially depolarizing channels acting independently on each subsystem. Surprisingly, we find that the robustness of (GHZ) entanglement increases with the number of qubits. An n-qubit Greenberger-Horne-Zeilinger (GHZ) state can stand more than 55% local depolarization in the limit n\ensuremath→\ensuremath∞.\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}.n\ensuremath→\ensuremath∞. GHZ states are more robust than other generic states of three and four qubits. We also study spin-squeezed states in the limit n\ensuremath→\ensuremath∞\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}n\ensuremath→\ensuremath∞ and find that they too can stand considerable local depolarization.
We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystem. To be specific, we consider an NNN-qubit Greenberger-Horne-Zeilinger (GHZ) state under a depolarization, dephasing, or dissipation channel, and examine nonlocality by testing violation of the Mermin-Klyshko inequality, which is one of Bell's inequalities for multiqubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an NNN-qubit GHZ state with even NNN is extremely persistent against dephasing.
We study the robustness of the Greenberger-Horne-Zeilinger (``cat'') class of multipartite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of NNN-party entanglement is studied in the large NNN limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes large and (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.
We investigate the decay of entanglement, due to decoherence, of multiqubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness-optimization problem that only involves states equivalent, under local unitary transformations, to the Greenberger-Horne-Zeilinger ∣GHZ⟩|\text{GHZ}⟩∣GHZ⟩ state.
The N-qubit states of the W class, for N>10,N>10,N>10, lead to more robust (against noise admixture) violations of local realism, than the Greenberger-Horne-Zeilinger (GHZ) states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining $N\ensuremath{-}2$ qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.
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.