SAMOP 2021 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 9: Quantum Metrology

QI 9.4: Vortrag

Donnerstag, 23. September 2021, 12:00–12:15, H4

Time-energy uncertainty relation for noisy quantum metrology — •Philippe Faist¹, Mischa P. Woods², Victor V. Albert⁴, Joseph M Renes², Jens Eisert¹, and John Preskill^3,5 — ¹Freie Universität Berlin — ²ETH Zurich, Switzerland — ³Caltech, Pasadena, USA — ⁴JCQCI, NIST and University of Maryland, USA — ⁵AWS Center for Quantum Computing, USA

Quantum metrology has many applications to science and technology, including the detection of very weak forces and precise measurement of time. To sense time, one prepares an initial state of a clock system, allows the system to evolve as governed by a Hamiltonian H, and then performs a measurement to estimate the time elapsed. Here, we introduce and study a fundamental trade-off which relates the amount by which the application of a noise channel reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. 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 non-commuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise, which are weaker than the Knill-Laflamme error-correction conditions. We discuss applications of the trade-off relation to sensing using a quantum many-body probe subject to erasure or amplitude-damping noise.