This paper investigates the potential of utilizing super-space geometry as a framework for modeling quantum entanglement. Traditional entanglement theories primarily focus on particle interactions, while this work proposes a novel approach by embedding quantum entanglement within the structure of super-space geometry. We aim to develop a computational methodology that reveals the dynamic characteristics of entangled states through the lens of this geometric model. The core claim is that super-space geometry offers a unique and powerful means of capturing the non-local nature of quantum entanglement, providing a more precise and comprehensive understanding of its properties. This research explores the potential of this approach to address limitations in existing entanglement models.This paper investigates the potential of utilizing super-space geometry as a framework for modeling quantum entanglement. Traditional entanglement theories primarily focus on particle interactions, while this work proposes a novel approach by embedding quantum entanglement within the structure of super-space geometry. We aim to develop a computational methodology that reveals the dynamic characteristics of entangled states through the lens of this geometric model. The core claim is that super-space geometry offers a unique and powerful means of capturing the non-local nature of quantum entanglement, providing a more precise and comprehensive understanding of its properties. This research explores the potential of this approach to address limitations in existing entanglement models.

Sep 1, 20260 citations

Entanglement and the geometry of two qubits

J.E. Avron, O. Kenneth

arXiv:0807.0212Annals of PhysicsAug 18, 200832 citations

Super-Link Fragility in Asymmetric W-Class States under Quantum Noise

Sougata Bhattacharyya, Fatih Ozaydin, Sovik Roy

The asymmetric three-qubit W-class state $|\overline{W_3^L}\rangle$ defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric $|\overline{W_3^L}\rangle$ state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is $C_{VB} > C_W > C_{BB}$ . Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of $|\overline{W_3^L}\rangle$ vanishes at the finite threshold of parameter $γ$ . We term this reordering as the \textit{Super-Link Fragility Effect}. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with $C_W$ and $C_{VB}$ sharing the same sudden-death threshold for some value of the parameter p, while $C_{BB}$ disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in $W$ -class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.The asymmetric three-qubit W-class state $|\overline{W_3^L}\rangle$ defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric $|\overline{W_3^L}\rangle$ state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is $C_{VB} > C_W > C_{BB}$. Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of $|\overline{W_3^L}\rangle$ vanishes at the finite threshold of parameter $γ$. We term this reordering as the \textit{Super-Link Fragility Effect}. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with $C_W$ and $C_{VB}$ sharing the same sudden-death threshold for some value of the parameter p, while $C_{BB}$ disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in $W$-class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.

quant-pharXiv:2606.12307Jun 11, 20260 citations

Geometry of quantum state space and entanglement

Prasenjit Deb, Pratapaditya Bej

arXiv:1805.11292Quantum Information ProcessingJan 28, 20193 citations

Quantum entanglement in multi-qubit systems

최정운

Jan 1, 20040 citations

Entangled States in a Single-Qubit Structure with SQUID Coupled with a Super-conducting Resonator

Liang Bao-Long, Ji‐Suo Wang, Meng Xiang-Guo

In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a single-qubit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a single-qubit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.

Communications in Theoretical PhysicsJan 1, 20081 citation

The asymmetric three-qubit W-class state

|\overline{W_3^L}\rangle

defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric

|\overline{W_3^L}\rangle

state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is

C_{VB} > C_W > C_{BB}

. Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of

|\overline{W_3^L}\rangle

vanishes at the finite threshold of parameter

γ

. We term this reordering as the \textit{Super-Link Fragility Effect}. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with

C_W

and

C_{VB}

sharing the same sudden-death threshold for some value of the parameter p, while

C_{BB}

disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in

W

-class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.