Multiparameter estimation for qubit states with collective measurements: a case study
Quantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2022-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ac599d |
| _version_ | 1797748476103098368 |
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| author | Yink Loong Len |
| author_facet | Yink Loong Len |
| author_sort | Yink Loong Len |
| collection | DOAJ |
| description | Quantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically prepared qubit states that is confined to a plane, where in order to obtain the optimal estimation precision for both parameters, collective measurements on multiple qubits are necessary. Upon treating N qubits as an ensemble of spin-1/2 systems, we show that simultaneous optimal estimation for both parameters can be attained asymptotically with a simple collective measurement strategy—first, we estimate the length parameter by measuring the populations in spaces corresponding to different total angular momentum values j , then we estimate the direction parameter by performing a spin projection onto an optimal basis. Furthermore, we show that when the state is nearly pure, for sufficiently but not arbitrarily large N , most information will be captured in the largest three j -subspaces. Then, we study how the total angular-momentum measurement can be realized by observing output signatures from a Bell multiport setup, either exactly for N = 2, 3, or approximately when the qubits are nearly pure for other N values. We also obtain numerical results that suggest that using a Bell multiport setup, one can distinguish between projection onto the j = N /2 and j = N /2 − 1 subspaces from their respective interference signatures at the output. |
| first_indexed | 2024-03-12T16:05:20Z |
| format | Article |
| id | doaj.art-28c06206b41640918ce8b4d50c85231b |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:05:20Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-28c06206b41640918ce8b4d50c85231b2023-08-09T14:21:25ZengIOP PublishingNew Journal of Physics1367-26302022-01-0124303303710.1088/1367-2630/ac599dMultiparameter estimation for qubit states with collective measurements: a case studyYink Loong Len0https://orcid.org/0000-0003-4810-3917Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw , Banacha 2c, 02-097, Warsaw, PolandQuantum estimation involving multiple parameters remains an important problem of both theoretical and practical interest. In this work, we study the problem of simultaneous estimation of two parameters that are respectively associate with the length and direction of the Bloch vector for identically prepared qubit states that is confined to a plane, where in order to obtain the optimal estimation precision for both parameters, collective measurements on multiple qubits are necessary. Upon treating N qubits as an ensemble of spin-1/2 systems, we show that simultaneous optimal estimation for both parameters can be attained asymptotically with a simple collective measurement strategy—first, we estimate the length parameter by measuring the populations in spaces corresponding to different total angular momentum values j , then we estimate the direction parameter by performing a spin projection onto an optimal basis. Furthermore, we show that when the state is nearly pure, for sufficiently but not arbitrarily large N , most information will be captured in the largest three j -subspaces. Then, we study how the total angular-momentum measurement can be realized by observing output signatures from a Bell multiport setup, either exactly for N = 2, 3, or approximately when the qubits are nearly pure for other N values. We also obtain numerical results that suggest that using a Bell multiport setup, one can distinguish between projection onto the j = N /2 and j = N /2 − 1 subspaces from their respective interference signatures at the output.https://doi.org/10.1088/1367-2630/ac599dmultiparameter estimationcollective measurementquantum metrologysuperresolution |
| spellingShingle | Yink Loong Len Multiparameter estimation for qubit states with collective measurements: a case study New Journal of Physics multiparameter estimation collective measurement quantum metrology superresolution |
| title | Multiparameter estimation for qubit states with collective measurements: a case study |
| title_full | Multiparameter estimation for qubit states with collective measurements: a case study |
| title_fullStr | Multiparameter estimation for qubit states with collective measurements: a case study |
| title_full_unstemmed | Multiparameter estimation for qubit states with collective measurements: a case study |
| title_short | Multiparameter estimation for qubit states with collective measurements: a case study |
| title_sort | multiparameter estimation for qubit states with collective measurements a case study |
| topic | multiparameter estimation collective measurement quantum metrology superresolution |
| url | https://doi.org/10.1088/1367-2630/ac599d |
| work_keys_str_mv | AT yinkloonglen multiparameterestimationforqubitstateswithcollectivemeasurementsacasestudy |