Time-averaged continuous quantum measurement
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912395868241920 |
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| author | Guilmin, Pierre Rouchon, Pierre Tilloy, Antoine |
| author_facet | Guilmin, Pierre Rouchon, Pierre Tilloy, Antoine |
| contents | The theory of continuous quantum measurement allows to reconstruct the state $ρ_t$ of a system from a continuous stochastic measurement record $I_t$. However, this truly continuous-time signal $I_t$ is never available in practice. In experiments, one generally has access to its digitization, i.e., to a series of time averages $I_k$ over finite intervals of duration $Δt$. In this letter, we take this digitization seriously and define $\barρ_n$ as the best Bayesian estimate of the quantum state given (only) a digitized record $(I_1,\dots,I_n)$. We show that $\barρ_{n+1}$ can be computed recursively from $I_{n+1}$ and $\barρ_n$ using an exact formula. The latter can be evaluated numerically exactly, or used as the basis for a perturbative expansion into successive powers of $\sqrt{Δt}$. This allows reconstructing quantum trajectories in regimes of coarse $Δt$ where existing methods fail, estimating parameters at fixed $Δt$ without bias, and directly sampling digitized quantum trajectories with schemes of arbitrarily high order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-averaged continuous quantum measurement Guilmin, Pierre Rouchon, Pierre Tilloy, Antoine Quantum Physics The theory of continuous quantum measurement allows to reconstruct the state $ρ_t$ of a system from a continuous stochastic measurement record $I_t$. However, this truly continuous-time signal $I_t$ is never available in practice. In experiments, one generally has access to its digitization, i.e., to a series of time averages $I_k$ over finite intervals of duration $Δt$. In this letter, we take this digitization seriously and define $\barρ_n$ as the best Bayesian estimate of the quantum state given (only) a digitized record $(I_1,\dots,I_n)$. We show that $\barρ_{n+1}$ can be computed recursively from $I_{n+1}$ and $\barρ_n$ using an exact formula. The latter can be evaluated numerically exactly, or used as the basis for a perturbative expansion into successive powers of $\sqrt{Δt}$. This allows reconstructing quantum trajectories in regimes of coarse $Δt$ where existing methods fail, estimating parameters at fixed $Δt$ without bias, and directly sampling digitized quantum trajectories with schemes of arbitrarily high order. |
| title | Time-averaged continuous quantum measurement |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.20382 |