Encoding parameters by measurement: Forgetting can be better in quantum metrology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909956997906432 |
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| author | Mondal, Shuva Ghosh, Priya Sen, Ujjwal |
| author_facet | Mondal, Shuva Ghosh, Priya Sen, Ujjwal |
| contents | We introduce quantum parameter estimation with the encoding being via a quantum measurement. We quantify the precision for estimating parameters characterizing a general two-outcome qubit measurement, considering two cases: when the outcomes of the encoding measurement are recorded and when the same are ignored. We find that in a large variety of such estimation scenarios, forgetting the outcomes yields higher precision. We derive a necessary criterion under which remembering the measurement outcomes provides better precision in comparison to the outcome-forgotten strategy. Furthermore, we establish a necessary and sufficient criterion for the simultaneous estimation of two parameters encoded by an arbitrary quantum process, including those involving measurements, using qubit probes, and find when the quantum Cramér$-$Rao bound is valid and achievable. For simultaneous estimation of two parameters characterizing the measurement, we find that the achievable quantum Cramér$-$Rao bound can be a valid precision bound only when the measurement direction depends on the parameters of interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Encoding parameters by measurement: Forgetting can be better in quantum metrology Mondal, Shuva Ghosh, Priya Sen, Ujjwal Quantum Physics We introduce quantum parameter estimation with the encoding being via a quantum measurement. We quantify the precision for estimating parameters characterizing a general two-outcome qubit measurement, considering two cases: when the outcomes of the encoding measurement are recorded and when the same are ignored. We find that in a large variety of such estimation scenarios, forgetting the outcomes yields higher precision. We derive a necessary criterion under which remembering the measurement outcomes provides better precision in comparison to the outcome-forgotten strategy. Furthermore, we establish a necessary and sufficient criterion for the simultaneous estimation of two parameters encoded by an arbitrary quantum process, including those involving measurements, using qubit probes, and find when the quantum Cramér$-$Rao bound is valid and achievable. For simultaneous estimation of two parameters characterizing the measurement, we find that the achievable quantum Cramér$-$Rao bound can be a valid precision bound only when the measurement direction depends on the parameters of interest. |
| title | Encoding parameters by measurement: Forgetting can be better in quantum metrology |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.10541 |