Heisenberg limit in phase measurements: the threshold detection approach
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912985910345728 |
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| author | Salykina, D. I. Liamin, V. S. Gorshenin, V. L. Nougmanov, B. N. Khalili, F. Ya. |
| author_facet | Salykina, D. I. Liamin, V. S. Gorshenin, V. L. Nougmanov, B. N. Khalili, F. Ya. |
| contents | The ultimate precision of phase estimation is limited by the Heisenberg scaling $Δϕ_0 = K/N$, where $K\sim1$ is a numerical prefactor and $N$ is the mean number of photons interacting with the phase shifting object(s). However, achieving this fundamental limit often comes at the cost of an extremely narrow high-sensitive range, rendering schemes impractical. We analyze the precision limits of phase measurements in single- and two-arm optical interferometers with input Gaussian states. We consider two detection methods: conventional homodyne measurement and non-Gaussian threshold detection that saturates the quantum Cramér-Rao bound.
We characterize the performance by two complementary metrics: the peak sensitivity $Δϕ_0$ and the width $δϕ$ of the high-sensitivity range. We demonstrate that Heisenberg scaling is attainable in all configurations considered. However, we reveal that $δϕ$ strongly depends on $K$. We derive an approximate analytic expression that describes this trade-off. We show also that the two-arm interferometer with antisymmetrically squeezed inputs exhibits exceptional performance, simultaneously achieving Heisenberg-limited sensitivity and a broad high-sensitivity range $δϕ=π/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heisenberg limit in phase measurements: the threshold detection approach Salykina, D. I. Liamin, V. S. Gorshenin, V. L. Nougmanov, B. N. Khalili, F. Ya. Quantum Physics The ultimate precision of phase estimation is limited by the Heisenberg scaling $Δϕ_0 = K/N$, where $K\sim1$ is a numerical prefactor and $N$ is the mean number of photons interacting with the phase shifting object(s). However, achieving this fundamental limit often comes at the cost of an extremely narrow high-sensitive range, rendering schemes impractical. We analyze the precision limits of phase measurements in single- and two-arm optical interferometers with input Gaussian states. We consider two detection methods: conventional homodyne measurement and non-Gaussian threshold detection that saturates the quantum Cramér-Rao bound. We characterize the performance by two complementary metrics: the peak sensitivity $Δϕ_0$ and the width $δϕ$ of the high-sensitivity range. We demonstrate that Heisenberg scaling is attainable in all configurations considered. However, we reveal that $δϕ$ strongly depends on $K$. We derive an approximate analytic expression that describes this trade-off. We show also that the two-arm interferometer with antisymmetrically squeezed inputs exhibits exceptional performance, simultaneously achieving Heisenberg-limited sensitivity and a broad high-sensitivity range $δϕ=π/2$. |
| title | Heisenberg limit in phase measurements: the threshold detection approach |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.06714 |