We investigate the influence of the initial mixture of qubits and the dissipation on the entanglement transfer from three-qubit Greenberger–Horne–Zeilinger (GHZ) and W state fields to three matter qubits, which are trapped in three spatially separated cavities. We find that at gt ≈11.07, the entanglement transfer can be almost complete no matter what state the qubits are initially prepared in. When the dissipation is taken into account, we find that the spontaneous emission plays the similar role to the cavity damping in the entanglement transfer, and the decay rate of the GHZ state is larger than that of the W state.We investigate the influence of the initial mixture of qubits and the dissipation on the entanglement transfer from three-qubit Greenberger–Horne–Zeilinger (GHZ) and W state fields to three matter qubits, which are trapped in three spatially separated cavities. We find that at gt ≈11.07, the entanglement transfer can be almost complete no matter what state the qubits are initially prepared in. When the dissipation is taken into account, we find that the spontaneous emission plays the similar role to the cavity damping in the entanglement transfer, and the decay rate of the GHZ state is larger than that of the W state.

Communications in Theoretical PhysicsDec 1, 20072 citations

Entanglement of mixed states in systems of n qubits

Renán Cabrera, W. E. Baylis

Bulletin of the American Physical SocietyJun 7, 20070 citations

Genuine entanglement under squeezed generalized amplitude damping channels with memory

Mazhar Ali

We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing, and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger–Horne–Zeilinger (GHZ) states and W states, mixed with white noise, and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state (with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter μ must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for n → ∞ are genuinely entangled.We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing, and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger–Horne–Zeilinger (GHZ) states and W states, mixed with white noise, and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state (with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter μ must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for n → ∞ are genuinely entangled.

arXiv:2401.15961Chinese Physics BJun 25, 20234 citations

Quantum entanglement in multi-qubit systems

최정운

Jan 1, 20040 citations

A measure for genuine tripartite entanglement

Shengjun Wu, Kaichen Zhong, Jeffery Wu

We introduce a real-valued functional $I(\vec{n}_1,\vec{n}_2)$ of four three-qubit correlations that turns the Greenberger-Horne-Zeilinger (GHZ) algebraic paradox into a quantitative witness of genuine tripartite entanglement. For every three-qubit state $ρ$ and every pair of directions, $|I(\vec{n}_1,\vec{n}_2;ρ)|\le 2$ , with equality if and only if $\vec{n}_1\perp\vec{n}_2$ and $ρ$ is locally unitarily equivalent to the GHZ state. On the five-parameter Acín family, $I(\hat{x},\hat{y})$ depends only on $λ_0λ_4$ and is maximised by the GHZ state; for the W state $I(\hat{x},\hat{y})=0$ and $\max|I_{\mathrm{W}}|=35/27$ . Maximising over independent local orthonormal frames yields a local-unitary invariant measure $\mathcal{E}_{\mathrm{GHZ}}\in[0,1]$ , computable from four three-body Pauli correlators, that equals one exactly on the GHZ orbit and takes the values $35/54$ on the W state and $1/2$ on product states. We show that $\mathcal{E}_{\mathrm{GHZ}}$ is not convex: an equal mixture of three biseparable states has $\mathcal{E}_{\mathrm{GHZ}}=14/27$ , larger than the average $1/2$ of its components. We also relate $\mathcal{E}_{\mathrm{GHZ}}$ to GHZ fidelity witnesses, discuss its behaviour under local operations and classical communication, and outline a generalisation to three qudits via Heisenberg-Weyl operators.We introduce a real-valued functional $I(\vec{n}_1,\vec{n}_2)$ of four three-qubit correlations that turns the Greenberger-Horne-Zeilinger (GHZ) algebraic paradox into a quantitative witness of genuine tripartite entanglement. For every three-qubit state $ρ$ and every pair of directions, $|I(\vec{n}_1,\vec{n}_2;ρ)|\le 2$, with equality if and only if $\vec{n}_1\perp\vec{n}_2$ and $ρ$ is locally unitarily equivalent to the GHZ state. On the five-parameter Acín family, $I(\hat{x},\hat{y})$ depends only on $λ_0λ_4$ and is maximised by the GHZ state; for the W state $I(\hat{x},\hat{y})=0$ and $\max|I_{\mathrm{W}}|=35/27$. Maximising over independent local orthonormal frames yields a local-unitary invariant measure $\mathcal{E}_{\mathrm{GHZ}}\in[0,1]$, computable from four three-body Pauli correlators, that equals one exactly on the GHZ orbit and takes the values $35/54$ on the W state and $1/2$ on product states. We show that $\mathcal{E}_{\mathrm{GHZ}}$ is not convex: an equal mixture of three biseparable states has $\mathcal{E}_{\mathrm{GHZ}}=14/27$, larger than the average $1/2$ of its components. We also relate $\mathcal{E}_{\mathrm{GHZ}}$ to GHZ fidelity witnesses, discuss its behaviour under local operations and classical communication, and outline a generalisation to three qudits via Heisenberg-Weyl operators.

quant-pharXiv:2605.02876Chinese Physics BMay 5, 20260 citations

We introduce a real-valued functional

I(\vec{n}_1,\vec{n}_2)

of four three-qubit correlations that turns the Greenberger-Horne-Zeilinger (GHZ) algebraic paradox into a quantitative witness of genuine tripartite entanglement. For every three-qubit state

ρ

and every pair of directions,

|I(\vec{n}_1,\vec{n}_2;ρ)|\le 2

, with equality if and only if

\vec{n}_1\perp\vec{n}_2

and

ρ

is locally unitarily equivalent to the GHZ state. On the five-parameter Acín family,

I(\hat{x},\hat{y})

depends only on

λ_0λ_4

and is maximised by the GHZ state; for the W state

I(\hat{x},\hat{y})=0

and

\max|I_{\mathrm{W}}|=35/27

. Maximising over independent local orthonormal frames yields a local-unitary invariant measure

\mathcal{E}_{\mathrm{GHZ}}\in[0,1]

, computable from four three-body Pauli correlators, that equals one exactly on the GHZ orbit and takes the values

35/54

on the W state and

1/2

on product states. We show that

\mathcal{E}_{\mathrm{GHZ}}

is not convex: an equal mixture of three biseparable states has

\mathcal{E}_{\mathrm{GHZ}}=14/27

, larger than the average

1/2

of its components. We also relate

\mathcal{E}_{\mathrm{GHZ}}

to GHZ fidelity witnesses, discuss its behaviour under local operations and classical communication, and outline a generalisation to three qudits via Heisenberg-Weyl operators.