Unitary dynamics and resource trade-offs in a four-qubit isotropic Heisenberg XXX chain with tunable next-nearest-neighbor coupling
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909025143095296 |
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| author | Khansari, Seyed Mohsen Moosavi |
| author_facet | Khansari, Seyed Mohsen Moosavi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04429 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unitary dynamics and resource trade-offs in a four-qubit isotropic Heisenberg XXX chain with tunable next-nearest-neighbor coupling Khansari, Seyed Mohsen Moosavi Quantum Physics 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. |
| title | Unitary dynamics and resource trade-offs in a four-qubit isotropic Heisenberg XXX chain with tunable next-nearest-neighbor coupling |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.04429 |