Type of Publication:  Journal article 
Publication status:  Published 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:3522ihuf5v99e65e2 
Author:  Ochoa, Maicol A.; Belzig, Wolfgang; Nitzan, Abraham 
Year of publication:  2017 
Published in:  Scientific Reports ; 8 (2017).  15781.  eISSN 20452322 
ArXivID:  arXiv:1707.08276 
DOI (citable link):  https://dx.doi.org/10.1038/s41598018335620 
Summary: 
In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A full description of such measurement should describe the measurement protocol and provide an explicit form of the measurement operator that transform the quantum state to its post measurement form. A simultaneous measurement of noncommuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator often used to model a weak measurement of a single observable is obtained by projecting a na\"ive extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the positionmomentum space. Finally, we show that the soobtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened.

Subject (DDC):  530 Physics 
Link to License:  Attribution 4.0 International 
Bibliography of Konstanz:  Yes 
Refereed:  Yes 
OCHOA, Maicol A., Wolfgang BELZIG, Abraham NITZAN, 2017. Simultaneous weak measurement of noncommuting observables : a generalized ArthursKelly protocol. In: Scientific Reports. 8, 15781. eISSN 20452322. Available under: doi: 10.1038/s41598018335620
@article{Ochoa20170726T02:25:25ZSimul39705.2, title={Simultaneous weak measurement of noncommuting observables : a generalized ArthursKelly protocol}, year={2017}, doi={10.1038/s41598018335620}, volume={8}, journal={Scientific Reports}, author={Ochoa, Maicol A. and Belzig, Wolfgang and Nitzan, Abraham}, note={Article Number: 15781} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22rdfsyntaxns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digitalrepositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.unikonstanz.de/rdf/resource/123456789/39705.2"> <dc:creator>Nitzan, Abraham</dc:creator> <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/> <dc:contributor>Belzig, Wolfgang</dc:contributor> <dcterms:issued>20170726T02:25:25Z</dcterms:issued> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:abstract xml:lang="eng">In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A full description of such measurement should describe the measurement protocol and provide an explicit form of the measurement operator that transform the quantum state to its post measurement form. A simultaneous measurement of noncommuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator often used to model a weak measurement of a single observable is obtained by projecting a na\"ive extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the positionmomentum space. Finally, we show that the soobtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened.</dcterms:abstract> <bibo:uri rdf:resource="https://kops.unikonstanz.de/handle/123456789/39705.2"/> <dc:contributor>Ochoa, Maicol A.</dc:contributor> <dc:creator>Ochoa, Maicol A.</dc:creator> <dc:creator>Belzig, Wolfgang</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20181025T13:12:30Z</dc:date> <dcterms:title>Simultaneous weak measurement of noncommuting observables : a generalized ArthursKelly protocol</dcterms:title> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:language>eng</dc:language> <dspace:hasBitstream rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/39705.2/3/Ochoa_2ihuf5v99e65e2.pdf"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20181025T13:12:30Z</dcterms:available> <dc:rights>Attribution 4.0 International</dc:rights> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/41"/> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/41"/> <dcterms:hasPart rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/39705.2/3/Ochoa_2ihuf5v99e65e2.pdf"/> <dc:contributor>Nitzan, Abraham</dc:contributor> </rdf:Description> </rdf:RDF>
Ochoa_2ihuf5v99e65e2.pdf  185 