Abstract It is proposed that how to generate and amplify multipartite entanglement simply by applying two microwave parametric amplifiers (MPAs) in a cascaded system without parametric downconversion interactions. Both the bipartite and tripartite entanglement of the three‐mode bosonic system are induced via the nonlinear gain of the two MPAs, which does not require strong coherent parametric coupling. Simultaneously, the intrinsic dissipation and detuning of the quadrature modes are corrected by modulating the phase difference of the MPAs, which directly changes the photon statistical distribution of the microwave cavity, so that both bipartite and tripartite entanglement of the dual‐cavity‐magnon system can be significantly enhanced. In particular, the phase‐modulated (PM) tripartite entanglement reaches the degree of 0.1 and breaks the limit of weak tripartite entanglement (on the degree of 0.01 and 0.001), which is a milestone breakthrough. More importantly, the PM multipartite entanglement is axisymmetric or centrosymmetric with respect to detuning and phase difference, which provides a bidirectional parameter selection for the experimental preparation of strong steady‐state entanglement. Furthermore, the PM multipartite entanglement is accompanied by improved robustness against the thermal bath temperature. The phase modulation mechanism can be potentially applied to construct stable multipartite entanglement networks and quantum information processing.Abstract It is proposed that how to generate and amplify multipartite entanglement simply by applying two microwave parametric amplifiers (MPAs) in a cascaded system without parametric downconversion interactions. Both the bipartite and tripartite entanglement of the three‐mode bosonic system are induced via the nonlinear gain of the two MPAs, which does not require strong coherent parametric coupling. Simultaneously, the intrinsic dissipation and detuning of the quadrature modes are corrected by modulating the phase difference of the MPAs, which directly changes the photon statistical distribution of the microwave cavity, so that both bipartite and tripartite entanglement of the dual‐cavity‐magnon system can be significantly enhanced. In particular, the phase‐modulated (PM) tripartite entanglement reaches the degree of 0.1 and breaks the limit of weak tripartite entanglement (on the degree of 0.01 and 0.001), which is a milestone breakthrough. More importantly, the PM multipartite entanglement is axisymmetric or centrosymmetric with respect to detuning and phase difference, which provides a bidirectional parameter selection for the experimental preparation of strong steady‐state entanglement. Furthermore, the PM multipartite entanglement is accompanied by improved robustness against the thermal bath temperature. The phase modulation mechanism can be potentially applied to construct stable multipartite entanglement networks and quantum information processing.

Advanced Quantum TechnologiesJun 11, 20250 citations

Genuine Measure of Multipartite Entanglement and its Monogamy Relation.

Yu Jing Guo, Lin Zhang

Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for defining multipartite entanglement measure (MEM): apart from the postulates of bipartite measure [i.e., vanishing on separable and nonincreasing under local operations and classical communication (LOCC)], a genuine MEM should additionally satisfy the \textit{unification condition} and the \textit{hierarchy condition}. We then come up with a \textit{complete monogamy formula} under the unified MEM (an MEM is called a unified MEM if it satisfies the unification condition). Consequently, we propose MEMs which are multipartite extensions of entanglement of formation (EoF), concurrence, tangle, the convex-roof extension of negativity and negativity, respectively. We show that multipartite extensions of the bipartite measures that are defined by the convex-roof structure are completely monogamous, the extensions of EoF, concurrence and tangle are genuine MEMs (an MEM is called a genuine MEM if it satisfies both the unification condition and the hierarchy condition), and multipartite extensions of both negativity and the convex-roof extension of negativity are unified MEMs but not genuine MEMs.Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for defining multipartite entanglement measure (MEM): apart from the postulates of bipartite measure [i.e., vanishing on separable and nonincreasing under local operations and classical communication (LOCC)], a genuine MEM should additionally satisfy the \textit{unification condition} and the \textit{hierarchy condition}. We then come up with a \textit{complete monogamy formula} under the unified MEM (an MEM is called a unified MEM if it satisfies the unification condition). Consequently, we propose MEMs which are multipartite extensions of entanglement of formation (EoF), concurrence, tangle, the convex-roof extension of negativity and negativity, respectively. We show that multipartite extensions of the bipartite measures that are defined by the convex-roof structure are completely monogamous, the extensions of EoF, concurrence and tangle are genuine MEMs (an MEM is called a genuine MEM if it satisfies both the unification condition and the hierarchy condition), and multipartite extensions of both negativity and the convex-roof extension of negativity are unified MEMs but not genuine MEMs.

Aug 22, 20190 citations

Bipartite Entanglement

John Watrous

Cambridge University Press eBooksMay 17, 20181 citation

Review: Bipartite Entanglement

Songbo Xie

Springer thesesJan 1, 20250 citations

Quantum Teleportation, Wavefunction Collapse, and Entanglement Advances — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Quantum energy teleportation (QET) demonstrated on superconducting hardware; single-photon double-slit confirms wavefunction collapse; W-state entanglement breakthroughs for networks. | MATH: QET protocol uses local operations and classical communication (LOCC) with energy extracted via conditional feedback — key operator: $\rho \to \sum_i K_i \rho K_i^\dagger$ with Kraus operators $K_i = \langle i| U |\psi\rangle$ ; energy teleportation gain $\Delta E = \text{Tr}[\rho H] - \text{Tr}[\rho' H] > 0$ requires negative conditional energy $\langle H_B \rangle_{\text{cond}} < 0$ . Double-slit: visibility $V = (I_{\max} - I_{\min})/(I_{\max} + I_{\min})$ , complementarity $V^2 + D^2 \leq 1$ (D = distinguishability). W-state: $|W\rangle = (|100\rangle + |010\rangle + |001\rangle)/\sqrt{3}$ — symmetric under particle permutations, maximal multipartite entanglement. | CONNECTION: W-state normalization $1/\sqrt{3}$ links to triangular lattice coordination num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Quantum energy teleportation (QET) demonstrated on superconducting hardware; single-photon double-slit confirms wavefunction collapse; W-state entanglement breakthroughs for networks. | MATH: QET protocol uses local operations and classical communication (LOCC) with energy extracted via conditional feedback — key operator: $ \rho \to \sum_i K_i \rho K_i^\dagger $ with Kraus operators $ K_i = \langle i| U |\psi\rangle $; energy teleportation gain $ \Delta E = \text{Tr}[\rho H] - \text{Tr}[\rho' H] > 0 $ requires negative conditional energy $ \langle H_B \rangle_{\text{cond}} < 0 $. Double-slit: visibility $ V = (I_{\max} - I_{\min})/(I_{\max} + I_{\min}) $, complementarity $ V^2 + D^2 \leq 1 $ (D = distinguishability). W-state: $ |W\rangle = (|100\rangle + |010\rangle + |001\rangle)/\sqrt{3} $ — symmetric under particle permutations, maximal multipartite entanglement. | CONNECTION: W-state normalization $ 1/\sqrt{3} $ links to triangular lattice coordination num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 21, 20260 citations

\rho \to \sum_i K_i \rho K_i^\dagger

with Kraus operators

K_i = \langle i| U |\psi\rangle

; energy teleportation gain

\Delta E = \text{Tr}[\rho H] - \text{Tr}[\rho' H] > 0

requires negative conditional energy

\langle H_B \rangle_{\text{cond}} < 0

. Double-slit: visibility

V = (I_{\max} - I_{\min})/(I_{\max} + I_{\min})

, complementarity

V^2 + D^2 \leq 1

(D = distinguishability). W-state:

|W\rangle = (|100\rangle + |010\rangle + |001\rangle)/\sqrt{3}

— symmetric under particle permutations, maximal multipartite entanglement. | CONNECTION: W-state normalization

1/\sqrt{3}

links to triangular lattice coordination num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com