Unitary dynamics and resource trade-offs in a four-qubit isotropic Heisenberg XXX chain with tunable next-nearest-neighbor coupling

• URL: http://arxiv.org/abs/2605.04429v2
• Date: Thu, 07 May 2026 23:05:44 GMT
• Title: Unitary dynamics and resource trade-offs in a four-qubit isotropic Heisenberg XXX chain with tunable next-nearest-neighbor coupling
• Abstract summary: This study derives the unitary dynamics of a four qubit Heisenberg XXX chain with tunable next nearest neighbor coupling $$.<n>We provide closed form expressions for fidelity $F((0),(t))$, coherence $C_l_1((t))$, and two qubit entanglement of formation $E_F(t)$ for subsystems $12$ and $34$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: This study derives the unitary dynamics of a four qubit Heisenberg XXX chain with tunable next nearest neighbor coupling $α$, starting from a Bell type initial state, and analyzes the evolution of quantum resources under the phase $φ= (α+ 1)t$. We provide closed form expressions for fidelity $F(ρ(0),ρ(t))$, coherence $C_{l_1}(ρ(t))$, and two qubit entanglement of formation $E_F(t)$ for subsystems $12$ and $34$, all of which are governed by $φ$. Fidelity exhibits periodic behavior with $F = \lvert \cos(φ/2) \rvert$ and a frozen regime at $α= -1$ where $F \equiv 1$. Coherence follows $C_{l_1}(ρ(t)) = \sin^2(φ/2)$, showing increasing sensitivity with $\lvert α+ 1 \rvert$ and vanishing at $α= -1$. Entanglement of formation $E_F(t)$ is an entropic function of $φ$, displaying banded oscillations and freezing at $α= -1$. The phase $φ$ unifies the behavior of all diagnostics, linking faster dynamics to larger $\lvert α+ 1 \rvert$ and revealing maximal sensitivity at $(α+ 1)t = π/4 + kπ/2$. This integrated framework provides exact benchmarks for small quantum devices and a clear pathway to noise, finite temperature, and larger system extensions.

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