General theory of measurement with two copies of a quantum state
We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outco...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00319007_v103_n4_p_Bendersky |
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todo:paper_00319007_v103_n4_p_Bendersky2023-10-03T14:42:05Z General theory of measurement with two copies of a quantum state Bendersky, A. Paz, J.P. Cunha, M.T. Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps Cμ such that the probability Prob(μ) is the fidelity of each map, i.e., Prob(μ)=Tr[ρCμ(ρ)]. Here, the map Cμ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure). © 2009 The American Physical Society. Fil:Bendersky, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paz, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00319007_v103_n4_p_Bendersky |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory |
| spellingShingle |
Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory Bendersky, A. Paz, J.P. Cunha, M.T. General theory of measurement with two copies of a quantum state |
| topic_facet |
Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory |
| description |
We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps Cμ such that the probability Prob(μ) is the fidelity of each map, i.e., Prob(μ)=Tr[ρCμ(ρ)]. Here, the map Cμ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure). © 2009 The American Physical Society. |
| format |
JOUR |
| author |
Bendersky, A. Paz, J.P. Cunha, M.T. |
| author_facet |
Bendersky, A. Paz, J.P. Cunha, M.T. |
| author_sort |
Bendersky, A. |
| title |
General theory of measurement with two copies of a quantum state |
| title_short |
General theory of measurement with two copies of a quantum state |
| title_full |
General theory of measurement with two copies of a quantum state |
| title_fullStr |
General theory of measurement with two copies of a quantum state |
| title_full_unstemmed |
General theory of measurement with two copies of a quantum state |
| title_sort |
general theory of measurement with two copies of a quantum state |
| url |
http://hdl.handle.net/20.500.12110/paper_00319007_v103_n4_p_Bendersky |
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AT benderskya generaltheoryofmeasurementwithtwocopiesofaquantumstate AT pazjp generaltheoryofmeasurementwithtwocopiesofaquantumstate AT cunhamt generaltheoryofmeasurementwithtwocopiesofaquantumstate |
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