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- Publisher Website: 10.1103/PhysRevA.72.042338
- Scopus: eid_2-s2.0-28844480109
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Article: Optimal estimation of group transformations using entanglement
Title | Optimal estimation of group transformations using entanglement |
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Authors | |
Issue Date | 2005 |
Publisher | American Physical Society. The Journal's web site is located at http://journals.aps.org/pra/ |
Citation | Physical Review A (Atomic, Molecular and Optical Physics), 2005, v. 72 n. 4, article no. 042338 How to Cite? |
Abstract | We derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined in a Bayesian sense, as minimization of the average value of a given cost function. We introduce a class of cost functions that generalizes the Holevo class for phase estimation, and show that for states of the optimal form all functions in such a class lead to the same optimal measurement. As a first application of the main result is the complete proof of the optimal efficiency in the transmission of a Cartesian reference frame. As a second application, we derive the optimal estimation of a completely unknown two-qubit maximally entangled state, provided that N copies of the state are available. In the limit of large N, the fidelity of the optimal estimation is shown to be 1-3/(4N). © 2005 The American Physical Society. |
Persistent Identifier | http://hdl.handle.net/10722/212845 |
ISSN | 2014 Impact Factor: 2.808 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chiribella, G. | - |
dc.contributor.author | D'Ariano, G. M. | - |
dc.contributor.author | Sacchi, M. F. | - |
dc.date.accessioned | 2015-07-28T04:05:12Z | - |
dc.date.available | 2015-07-28T04:05:12Z | - |
dc.date.issued | 2005 | - |
dc.identifier.citation | Physical Review A (Atomic, Molecular and Optical Physics), 2005, v. 72 n. 4, article no. 042338 | - |
dc.identifier.issn | 1050-2947 | - |
dc.identifier.uri | http://hdl.handle.net/10722/212845 | - |
dc.description.abstract | We derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined in a Bayesian sense, as minimization of the average value of a given cost function. We introduce a class of cost functions that generalizes the Holevo class for phase estimation, and show that for states of the optimal form all functions in such a class lead to the same optimal measurement. As a first application of the main result is the complete proof of the optimal efficiency in the transmission of a Cartesian reference frame. As a second application, we derive the optimal estimation of a completely unknown two-qubit maximally entangled state, provided that N copies of the state are available. In the limit of large N, the fidelity of the optimal estimation is shown to be 1-3/(4N). © 2005 The American Physical Society. | - |
dc.language | eng | - |
dc.publisher | American Physical Society. The Journal's web site is located at http://journals.aps.org/pra/ | - |
dc.relation.ispartof | Physical Review A (Atomic, Molecular and Optical Physics) | - |
dc.title | Optimal estimation of group transformations using entanglement | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1103/PhysRevA.72.042338 | - |
dc.identifier.scopus | eid_2-s2.0-28844480109 | - |
dc.identifier.volume | 72 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | article no. 042338 | - |
dc.identifier.epage | article no. 042338 | - |
dc.identifier.eissn | 1094-1622 | - |
dc.identifier.isi | WOS:000232931800072 | - |
dc.identifier.issnl | 1050-2947 | - |