Beating noise with abstention in state estimation
We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consist of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allo...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2012-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/14/10/105015 |
| _version_ | 1797751666745802752 |
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| author | Bernat Gendra Elio Ronco-Bonvehi John Calsamiglia Ramon Muñoz-Tapia Emilio Bagan |
| author_facet | Bernat Gendra Elio Ronco-Bonvehi John Calsamiglia Ramon Muñoz-Tapia Emilio Bagan |
| author_sort | Bernat Gendra |
| collection | DOAJ |
| description | We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consist of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allows for inconclusive answers, or abstentions. We present the optimal protocol and compute its fidelity for a given probability of abstention. The improvement over standard estimation, without abstention, can be viewed as an effective noise reduction. These and other results are illustrated for small values of N . For asymptotically large N , we derive analytical expressions of the fidelity and the probability of abstention and show that for a fixed fidelity gain the latter decreases with N at an exponential rate given by a Kulback–Leibler (relative) entropy. As a byproduct, we give an asymptotic expression in terms of this very entropy of the probability that a system of N qubits, all prepared in the same state, has a given total angular momentum. We also discuss an extreme situation where noise increases with N and where estimation with abstention provides the most significant improvement as compared to the standard approach. |
| first_indexed | 2024-03-12T16:52:54Z |
| format | Article |
| id | doaj.art-aba2c3e05bbe46648abed4449b066263 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:52:54Z |
| publishDate | 2012-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-aba2c3e05bbe46648abed4449b0662632023-08-08T11:06:41ZengIOP PublishingNew Journal of Physics1367-26302012-01-01141010501510.1088/1367-2630/14/10/105015Beating noise with abstention in state estimationBernat Gendra0Elio Ronco-Bonvehi1John Calsamiglia2Ramon Muñoz-Tapia3Emilio Bagan4Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona , 08193 Bellaterra, Barcelona, SpainFísica Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona , 08193 Bellaterra, Barcelona, SpainFísica Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona , 08193 Bellaterra, Barcelona, SpainFísica Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona , 08193 Bellaterra, Barcelona, SpainFísica Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona , 08193 Bellaterra, Barcelona, SpainWe address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consist of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allows for inconclusive answers, or abstentions. We present the optimal protocol and compute its fidelity for a given probability of abstention. The improvement over standard estimation, without abstention, can be viewed as an effective noise reduction. These and other results are illustrated for small values of N . For asymptotically large N , we derive analytical expressions of the fidelity and the probability of abstention and show that for a fixed fidelity gain the latter decreases with N at an exponential rate given by a Kulback–Leibler (relative) entropy. As a byproduct, we give an asymptotic expression in terms of this very entropy of the probability that a system of N qubits, all prepared in the same state, has a given total angular momentum. We also discuss an extreme situation where noise increases with N and where estimation with abstention provides the most significant improvement as compared to the standard approach.https://doi.org/10.1088/1367-2630/14/10/105015 |
| spellingShingle | Bernat Gendra Elio Ronco-Bonvehi John Calsamiglia Ramon Muñoz-Tapia Emilio Bagan Beating noise with abstention in state estimation New Journal of Physics |
| title | Beating noise with abstention in state estimation |
| title_full | Beating noise with abstention in state estimation |
| title_fullStr | Beating noise with abstention in state estimation |
| title_full_unstemmed | Beating noise with abstention in state estimation |
| title_short | Beating noise with abstention in state estimation |
| title_sort | beating noise with abstention in state estimation |
| url | https://doi.org/10.1088/1367-2630/14/10/105015 |
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