Permutation-symmetric quantum trajectories

Elliot W. Lloyd; Aleksandra A. Ziolkowska; Jonathan Keeling

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arXiv · 2605.11103

Permutation-symmetric quantum trajectories

Elliot W. Lloyd·Aleksandra A. Ziolkowska·Jonathan Keeling

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Abstract

We show how one may perform a stochastic unravelling which respects weak permutation symmetry for general models of $N$ emitters coupled to a common system (e.g. a cavity mode). Our work extends prior work by Zhang et al. [2018 New J. Phys. 20 112001] which provided an efficient quantum jump approach for a restricted subset of such problems. For problems involving $2$-level emitters, such an unravelling reduces the computational cost from $\mathcal{O}(N^5)$ to $\mathcal{O}(N^2)$, and with additional refinements, allows reduction to $\mathcal{O}(N)$. This significantly increases the range of system sizes for which one can model exact quantum dynamics of such systems. We further show how the method can also be applied to $d$-level systems, with computational effort scaling as $\mathcal{O}(N^{d(d-1)/2})$, and we show it allows large-$N$ simulations for $d=3$.

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Elliot W. Lloyd, Aleksandra A. Ziolkowska, Jonathan Keeling. 2026-05-11. Permutation-symmetric quantum trajectories. https://arxiv.org/abs/2605.11103

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