Haar-random and pretty good measurements for Bayesian state estimation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910472197898240 |
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| author | Quadeer, Maria |
| author_facet | Quadeer, Maria |
| contents | We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given $N$ Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states. For ensembles of mixed qubit states, we find that measurements defined through unitary 2-designs closely approximate those defined via Haar random unitaries while the Pauli group only gives a weak lower bound. For a single-shot-update, we show using the Petz recovery map for pretty good measurement that it can give pretty good Bayesian mean estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20565 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Haar-random and pretty good measurements for Bayesian state estimation Quadeer, Maria Quantum Physics Mathematical Physics We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given $N$ Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states. For ensembles of mixed qubit states, we find that measurements defined through unitary 2-designs closely approximate those defined via Haar random unitaries while the Pauli group only gives a weak lower bound. For a single-shot-update, we show using the Petz recovery map for pretty good measurement that it can give pretty good Bayesian mean estimates. |
| title | Haar-random and pretty good measurements for Bayesian state estimation |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2310.20565 |