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dc.contributor.author
Faist, Philippe
dc.contributor.author
Woods, Mischa P.
dc.contributor.author
Albert, Victor V.
dc.contributor.author
Renes, Joseph M.
dc.contributor.author
Eisert, Jens
dc.contributor.author
Preskill, John
dc.date.accessioned
2023-12-19T08:44:02Z
dc.date.available
2023-12-14T09:27:30Z
dc.date.available
2023-12-19T08:44:02Z
dc.date.issued
2023-12
dc.identifier.issn
2691-3399
dc.identifier.other
10.1103/PRXQuantum.4.040336
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/647543
dc.identifier.doi
10.3929/ethz-b-000647543
dc.description.abstract
Detection of very weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. To sense an unknown physical parameter, one prepares an initial state of a probe system, allows the probe to evolve as governed by a Hamiltonian H for some time t, and then measures the probe. If H is known, we can estimate t by this method; if t is known, we can estimate classical parameters on which H depends. The accuracy of a quantum sensor can be limited by either intrinsic quantum noise or by noise arising from the interactions of the probe with its environment. In this work, we introduce and study a fundamental trade-off, which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which a party Alice prepares an initial pure state of the clock, allows the clock to evolve for a time that is not precisely known, and then transmits the clock through a noisy channel to a party Bob. Meanwhile, the environment (Eve) receives any information about the clock that is lost during transmission. We prove that Bob's loss of quantum Fisher information about the elapsed time is equal to Eve's gain of quantum Fisher information about a complementary energy parameter. We also prove a similar, but more general, trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two noncommuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise, which form a subset of the Knill-Laflamme error-correction conditions. A state and its local time-evolution direction, if they satisfy these conditions, are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of the trade-off relation to sensing using a quantum many-body probe subject to erasure or amplitude-damping noise.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
American Physical Society
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.title
Time-Energy Uncertainty Relation for Noisy Quantum Metrology
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2023-12-05
ethz.journal.title
PRX Quantum
ethz.journal.volume
4
en_US
ethz.journal.issue
4
en_US
ethz.pages.start
040336
en_US
ethz.size
85 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.grant
The resource of time in quantum information theory
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
ethz.grant.agreementno
179914
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Ambizione
ethz.relation.isNewVersionOf
20.500.11850/592780
ethz.date.deposited
2023-12-14T09:27:30Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2023-12-19T08:44:07Z
ethz.rosetta.lastUpdated
2024-02-03T08:06:52Z
ethz.rosetta.versionExported
true
ethz.COinS
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