Heisenberg-limited continuous-variable distributed quantum metrology with arbitrary weights
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909541253251072 |
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| author | Ge, Wenchao Jacobs, Kurt |
| author_facet | Ge, Wenchao Jacobs, Kurt |
| contents | Distributed quantum metrology (DQM) enables the estimation of global functions of d distributed parameters beyond the capability of separable sensors. Continuous-variable DQM involves using a linear network with at least one nonclassical input. Here we fully elucidate the structure of linear networks with two non-vacuum inputs which allows us to prove a number of fundamental properties of continuous-variable DQM. While measuring the sum of d parameters at the Heisenberg limit can be achieved with a single non-vacuum input, we show that two inputs, one of which can be classical, is required to measure an arbitrary linear combination of d parameters and an arbitrary global function of the parameters. We obtain a universal and tight upper bound on the sensitivity of DQM networks with two inputs, and completely characterize the properties of the nonclassical input required to obtain a quantum advantage. This reveals that a wide range of nonclassical states make this possible, including a squeezed vacuum. We also show that for a class of nonclassical inputs local photon number detection will achieve the maximum sensitivity. Finally we show that a general DQM network has two distinct regimes. The first achieves Heisenberg scaling. In the second the nonclassical input is much weaker than the coherent input, nevertheless providing a multiplicative enhancement to the otherwise classical sensitivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heisenberg-limited continuous-variable distributed quantum metrology with arbitrary weights Ge, Wenchao Jacobs, Kurt Quantum Physics Distributed quantum metrology (DQM) enables the estimation of global functions of d distributed parameters beyond the capability of separable sensors. Continuous-variable DQM involves using a linear network with at least one nonclassical input. Here we fully elucidate the structure of linear networks with two non-vacuum inputs which allows us to prove a number of fundamental properties of continuous-variable DQM. While measuring the sum of d parameters at the Heisenberg limit can be achieved with a single non-vacuum input, we show that two inputs, one of which can be classical, is required to measure an arbitrary linear combination of d parameters and an arbitrary global function of the parameters. We obtain a universal and tight upper bound on the sensitivity of DQM networks with two inputs, and completely characterize the properties of the nonclassical input required to obtain a quantum advantage. This reveals that a wide range of nonclassical states make this possible, including a squeezed vacuum. We also show that for a class of nonclassical inputs local photon number detection will achieve the maximum sensitivity. Finally we show that a general DQM network has two distinct regimes. The first achieves Heisenberg scaling. In the second the nonclassical input is much weaker than the coherent input, nevertheless providing a multiplicative enhancement to the otherwise classical sensitivity. |
| title | Heisenberg-limited continuous-variable distributed quantum metrology with arbitrary weights |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.01074 |