Beating noise with abstention in state estimation

We address the problem of estimating pure qubit states with nonideal (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 allow...

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Authors: Gendra Casalí, Bernat, Ronco Bonvehi, Elio, Calsamiglia, John|||0000-0003-1735-1360, Muñoz Tapia, Ramon|||0000-0002-3048-9236, Bagan, E.|||0000-0002-7900-3567
Format: article
Publication Date:2012
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:204035
Online Access:https://ddd.uab.cat/record/204035
https://dx.doi.org/urn:doi:10.1088/1367-2630/14/10/105015
Access Level:Open access
Keyword:Analytical expressions
Asymptotic expressions
Beating noise
Exponential rates
Fixed fidelity
Large N
N qubits
Nonideal
Optimal protocols
Qubit state
Standard estimation
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spelling Beating noise with abstention in state estimationGendra Casalí, BernatRonco Bonvehi, ElioCalsamiglia, John|||0000-0003-1735-1360Muñoz Tapia, Ramon|||0000-0002-3048-9236Bagan, E.|||0000-0002-7900-3567Analytical expressionsAsymptotic expressionsBeating noiseExponential ratesFixed fidelityLarge NN qubitsNonidealOptimal protocolsQubit stateStandard estimationWe address the problem of estimating pure qubit states with nonideal (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. 22012-01-0120122012-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/204035https://dx.doi.org/urn:doi:10.1088/1367-2630/14/10/105015reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 FIS2008-01236Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-0985open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra, i la creació d'obres derivades, sempre que no sigui amb finalitats comercials i que es distribueixin sota la mateixa llicència que regula l'obra original. Cal que es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2040352026-06-06T12:50:31Z
dc.title.none.fl_str_mv Beating noise with abstention in state estimation
title Beating noise with abstention in state estimation
spellingShingle Beating noise with abstention in state estimation
Gendra Casalí, Bernat
Analytical expressions
Asymptotic expressions
Beating noise
Exponential rates
Fixed fidelity
Large N
N qubits
Nonideal
Optimal protocols
Qubit state
Standard estimation
title_short 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_sort Beating noise with abstention in state estimation
dc.creator.none.fl_str_mv Gendra Casalí, Bernat
Ronco Bonvehi, Elio
Calsamiglia, John|||0000-0003-1735-1360
Muñoz Tapia, Ramon|||0000-0002-3048-9236
Bagan, E.|||0000-0002-7900-3567
author Gendra Casalí, Bernat
author_facet Gendra Casalí, Bernat
Ronco Bonvehi, Elio
Calsamiglia, John|||0000-0003-1735-1360
Muñoz Tapia, Ramon|||0000-0002-3048-9236
Bagan, E.|||0000-0002-7900-3567
author_role author
author2 Ronco Bonvehi, Elio
Calsamiglia, John|||0000-0003-1735-1360
Muñoz Tapia, Ramon|||0000-0002-3048-9236
Bagan, E.|||0000-0002-7900-3567
author2_role author
author
author
author
dc.subject.none.fl_str_mv Analytical expressions
Asymptotic expressions
Beating noise
Exponential rates
Fixed fidelity
Large N
N qubits
Nonideal
Optimal protocols
Qubit state
Standard estimation
topic Analytical expressions
Asymptotic expressions
Beating noise
Exponential rates
Fixed fidelity
Large N
N qubits
Nonideal
Optimal protocols
Qubit state
Standard estimation
description We address the problem of estimating pure qubit states with nonideal (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.
publishDate 2012
dc.date.none.fl_str_mv 2
2012-01-01
2012
2012-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/204035
https://dx.doi.org/urn:doi:10.1088/1367-2630/14/10/105015
url https://ddd.uab.cat/record/204035
https://dx.doi.org/urn:doi:10.1088/1367-2630/14/10/105015
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 FIS2008-01236
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-0985
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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