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| Formato: | Preprint |
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2023
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| Acceso en línea: | https://arxiv.org/abs/2308.05871 |
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| _version_ | 1866913351828766720 |
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| author | Volkoff, T. J. Ryu, Changhyun |
| author_facet | Volkoff, T. J. Ryu, Changhyun |
| contents | Parity or quadratic spin (e.g., $J_{z}^{2}$) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock input state allow to saturate the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles, but only when the interferometer phase $θ$ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at $θ=0$, whereas better-than-standard quantum limit performance of the $J_{z}^{2}$ readout is restricted to an $o(\sqrt{N})$ occupation imbalance. We show that a method of moments readout of two quadratic spin observables $J_{z}^{2}$ and $J_{+}^{2}+J_{-}^{2}$ is globally optimal for Dicke state probes, i.e., the error saturates the QFI for all $θ$. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states, showing that method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of $θ$ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four mode state $\vert {N\over 4},{N\over 4},{N\over 4},{N\over 4}\rangle$ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases $θ_{1}$, $θ_{2}$ (compared to independent probing of the MZ phases by two copies of $\vert {N\over 4},{N\over 4}\rangle$) appears when more than one particle is lost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05871 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Globally optimal interferometry with lossy twin Fock probes Volkoff, T. J. Ryu, Changhyun Quantum Physics Quantum Gases Mathematical Physics Parity or quadratic spin (e.g., $J_{z}^{2}$) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock input state allow to saturate the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles, but only when the interferometer phase $θ$ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at $θ=0$, whereas better-than-standard quantum limit performance of the $J_{z}^{2}$ readout is restricted to an $o(\sqrt{N})$ occupation imbalance. We show that a method of moments readout of two quadratic spin observables $J_{z}^{2}$ and $J_{+}^{2}+J_{-}^{2}$ is globally optimal for Dicke state probes, i.e., the error saturates the QFI for all $θ$. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states, showing that method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of $θ$ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four mode state $\vert {N\over 4},{N\over 4},{N\over 4},{N\over 4}\rangle$ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases $θ_{1}$, $θ_{2}$ (compared to independent probing of the MZ phases by two copies of $\vert {N\over 4},{N\over 4}\rangle$) appears when more than one particle is lost. |
| title | Globally optimal interferometry with lossy twin Fock probes |
| topic | Quantum Physics Quantum Gases Mathematical Physics |
| url | https://arxiv.org/abs/2308.05871 |