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:1310.7336 · Journal of Physics B Atomic Molecular and Optical Physics

Robustness of multiparticle entanglement: specific entanglement classes and random states

Mazhar Ali, Otfried Gühne

Published Feb 20, 2014• 25 citations
arXivHTMLPDF

Abstract

We investigate the robustness of genuine multiparticle entanglement under decoherence. We consider different kinds of entangled three- and four-qubit states as well as random pure states. For amplitude damping noise, we find that the W-type states are most robust, while other states are not more robust than generic states. For phase damping noise the GHZ state is the most robust state, and for depolarizing noise several states are significantly more robust than random states.

DOI
10.1088/0953-4075/47/5/055503

Related papers

Robustness of multiparticle entanglement: specific entanglement classes and random states

Mazhar Ali

We investigate the robustness of genuine multiparticle entanglement under decoherence. We consider different kinds of entangled three- and four-qubit states as well as random pure states. For amplitude damping noise, we find that the W-type states are most robust, while other states are not more robust than generic states. For phase damping noise the GHZ state is the most robust state, and for depolarizing noise several states are significantly more robust than random states.

•Aug 14, 2016•17 citations

Robustness of multiparty entanglement

Christoph Simon, Julia Kempe

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.

arXiv:quant-ph/0109102•Physical Review A•May 9, 2002•168 citations

Detecting the dimensionality of genuine multiparticle entanglement

Gabriele Cobucci, Armin Tavakoli

Complex forms of quantum entanglement can arise in two qualitatively different ways: either between many qubits or between two particles with higher-than-qubit dimension. While both the many-qubit frontier and the high-dimension frontier are well established, state-of-the-art quantum technology is becoming increasingly able to create and manipulate entangled states that simultaneously feature many particles and high dimension. Here, we investigate generic states that can be considered both genuinely high-dimensional and genuine multiparticle entangled. We consider a natural quantity that characterizes this key property. To detect it, we develop three different classes of criteria. These enable us both to probe the ultimate noise tolerance of this form of entanglement and to make detection schemes using sparse or even minimal measurement resources. The approach provides a simple way of benchmarking entanglement dimensionality in the multiparticle regime and general, platform-independent, detection methods that readily apply to experimental use.

arXiv:2402.06234•Science Advances•Sep 20, 2024•12 citations

Intraparticle entanglement in noisy quantum channels: degradation and revival through amplitude damping

Animesh Sinha Roy, C. V. Namitha, Subroto Mukerjee +2 more

Quantum correlations between two or more different degrees of freedom of the same particle are sometimes referred to as intraparticle entanglement. In this work, we study these intraparticle correlations between two different degrees of freedom under various decoherence channels, viz. amplitude damping, depolarizing, and phase damping channels. We mainly focus on the amplitude-damping channel for which we obtain an exact analytical expression for the concurrence of an arbitrary initial pure state. In this channel, we observe the unique feature of entanglement arising from a separable initial state. We show that this channel allows for a revival of entanglement with an increasing damping parameter, including from a zero value of the concurrence. We also consider the amplitude-damping channel for interparticle entanglement and show that it does not display any of the above-mentioned interesting features. Further, for comparable parameters, the decay of entanglement in the interparticle system is much greater than in the intraparticle system, which we also find to be true for the phase damping and depolarizing channels. Thus, intraparticle entanglement subjected to damping is much more robust than interparticle entanglement.

Frontiers in Quantum Science and Technology•Jun 18, 2025•2 citations

Characterizing Entanglement in Combinations of Bell States through Superposition and Mixing: An Increase in Entanglement on Introducing Depolarizing, Phase Damping, and Amplitude Damping Noise

Nishant Chaudhari, Jean-François Van Huele

We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.

quant-pharXiv:2608.17500•Aug 19, 2026•0 citations

Most Robust and Fragile States with the Same Entanglement Properties

Hongmei Li, Bao‐Kui Zhao

Abstract Finding the most robust entangled states and the most fragile entangled states during the whole process of decoherence is particularly a fundamental problem for quantum physics and quantum information processing. Here the robustness of three‐qubit states under three different decoherence channels (amplitude damping, dephasing, bit flip) systematically are investigated, and the most robust genuine tripartite entangled states and the most fragile ones during each of the three decoherence processes are found. Moreover, the states with the most significant difference in robustness are shown to be locally unitarily equivalent to each other and therefore contain the same entanglement properties.

Annalen der Physik•Sep 3, 2018•3 citations
We investigate the robustness of genuine multiparticle entanglement under decoherence. We consider different kinds of entangled three- and four-qubit states as well as random pure states. For amplitude damping noise, we find that the W-type states are most robust, while other states are not more robust than generic states. For phase damping noise the GHZ state is the most robust state, and for depolarizing noise several states are significantly more robust than random states.
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.
Complex forms of quantum entanglement can arise in two qualitatively different ways: either between many qubits or between two particles with higher-than-qubit dimension. While both the many-qubit frontier and the high-dimension frontier are well established, state-of-the-art quantum technology is becoming increasingly able to create and manipulate entangled states that simultaneously feature many particles and high dimension. Here, we investigate generic states that can be considered both genuinely high-dimensional and genuine multiparticle entangled. We consider a natural quantity that characterizes this key property. To detect it, we develop three different classes of criteria. These enable us both to probe the ultimate noise tolerance of this form of entanglement and to make detection schemes using sparse or even minimal measurement resources. The approach provides a simple way of benchmarking entanglement dimensionality in the multiparticle regime and general, platform-independent, detection methods that readily apply to experimental use.
Quantum correlations between two or more different degrees of freedom of the same particle are sometimes referred to as intraparticle entanglement. In this work, we study these intraparticle correlations between two different degrees of freedom under various decoherence channels, viz. amplitude damping, depolarizing, and phase damping channels. We mainly focus on the amplitude-damping channel for which we obtain an exact analytical expression for the concurrence of an arbitrary initial pure state. In this channel, we observe the unique feature of entanglement arising from a separable initial state. We show that this channel allows for a revival of entanglement with an increasing damping parameter, including from a zero value of the concurrence. We also consider the amplitude-damping channel for interparticle entanglement and show that it does not display any of the above-mentioned interesting features. Further, for comparable parameters, the decay of entanglement in the interparticle system is much greater than in the intraparticle system, which we also find to be true for the phase damping and depolarizing channels. Thus, intraparticle entanglement subjected to damping is much more robust than interparticle entanglement.
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
Abstract Finding the most robust entangled states and the most fragile entangled states during the whole process of decoherence is particularly a fundamental problem for quantum physics and quantum information processing. Here the robustness of three‐qubit states under three different decoherence channels (amplitude damping, dephasing, bit flip) systematically are investigated, and the most robust genuine tripartite entangled states and the most fragile ones during each of the three decoherence processes are found. Moreover, the states with the most significant difference in robustness are shown to be locally unitarily equivalent to each other and therefore contain the same entanglement properties.