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.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.

quant-pharXiv:2608.07723Aug 11, 20260 citations

Exploring a strongly non-Markovian behavior

Vasyl A. Alba, Gordon J Berman, William Bialek +1 more

Bulletin of the American Physical SocietyMar 15, 20170 citations

The non-Markovian stochastic Schrödinger equation for open systems

Lajos Diósi, Walter T. Strunz

We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one hand and coherent states on the other. The latter approach utilizes the analytical properties of coherent states and enables a microscopic interpretation of the stochastic states. The alternative first approach is based on the general description of open systems using path integrals as originated by Feynman and Vernon.We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one hand and coherent states on the other. The latter approach utilizes the analytical properties of coherent states and enables a microscopic interpretation of the stochastic states. The alternative first approach is based on the general description of open systems using path integrals as originated by Feynman and Vernon.

Jan 1, 1997143 citations

Probabilities and microscopic behaviors

Keith S. Stowe

Cambridge University Press eBooksMay 10, 20070 citations

Nonlocal Non-Markovian Effects

Dong Xie, An Min Wang

Dec 22, 20120 citations

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.