Emergent Non-Markovian Nonlinear Qubit From Collective Spin Interactions

• URL: http://arxiv.org/abs/2608.07723v1
• Date: Fri, 07 Aug 2026 19:23:40 GMT
• Title: Emergent Non-Markovian Nonlinear Qubit From Collective Spin Interactions
• Abstract summary: We show that a closed interacting many-body system can generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit.<n>We derive the leading finite-$N$ corrections to a nonlinear mean-field limit and show that they correspond to an emergent non-Markovian dephasing process.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, $H=χJ_z^2$, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-$N$ regime of this model has been extensively studied, the conventional fixed-$χ$ scaling does not yield a nontrivial dynamical large-$N$ limit. In this paper, we investigate a complementary large-$N$ formulation obtained from the double limit $N\rightarrow\infty$ and $χ\rightarrow O(g/N)$, where $g$ is a coupling constant. We derive the leading finite-$N$ corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale $t_\varphi\geq\sqrt{N}/(2g)$. Exact finite-$N$ calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.

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