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Time-Energy Uncertainty Relation for Noisy Quantum Metrology

Philippe Faist, Mischa P. Woods, Victor V. Albert +3 more

The impact of noise on the accuracy of a quantum clock is investigated, unveiling a necessary and sufficient requirement for accuracy that extends standard error-correcting conditions to quantum metrology.

arXiv:2207.13707PRX QuantumDec 5, 20239 citations

A derivation of the time-energy uncertainty relation

J S Briggs

Some of the difficulties that have occurred in the past associated with the derivation of a time-energy uncertainty relation are discussed. Then it is shown that, beginning with a time-independent quantum composite of system and environment, a time-energy uncertainty relation for the system alone can be derived in the limit that the environment becomes classical, to provide a classical clock with which to monitor the quantum system.

Journal of Physics Conference SeriesFeb 1, 200832 citations

Time-energy uncertainty relation for quantum events

Matteo Fadel, Lorenzo Maccone

Textbook quantum mechanics treats time as a classical parameter and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\mathrm{\ensuremath{\Delta}}t\mathrm{\ensuremath{\Delta}}E\ensuremath{\gtrsim}\ensuremath{\hbar}$, the term $\mathrm{\ensuremath{\Delta}}t$ must be interpreted as a time interval and not as a time measurement uncertainty due to quantum noise. However, quantum clocks allow for a measurement of the ``time at which an event happens'' by conditioning the system's evolution on an additional quantum degree of freedom. Within this framework we derive here two uncertainty relations that relate the uncertainty in the quantum measurement of the time at which a quantum event happens on a system to its energy uncertainty.Textbook quantum mechanics treats time as a classical parameter and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\mathrm{\ensuremath{\Delta}}t\mathrm{\ensuremath{\Delta}}E\ensuremath{\gtrsim}\ensuremath{\hbar}$, the term $\mathrm{\ensuremath{\Delta}}t$ must be interpreted as a time interval and not as a time measurement uncertainty due to quantum noise. However, quantum clocks allow for a measurement of the ``time at which an event happens'' by conditioning the system's evolution on an additional quantum degree of freedom. Within this framework we derive here two uncertainty relations that relate the uncertainty in the quantum measurement of the time at which a quantum event happens on a system to its energy uncertainty.

arXiv:2108.13974Physical Review ANov 24, 202110 citations

Noisy Quantum Metrology, Optical Interferometry, and the Time Duration of Physical Processes

Bruno M. Escher, Márcio M. Taddei, Nicim Zagury +2 more

We develop a general method of parameter estimation for noisy systems, which leads to useful bounds for optical interferometry and the time duration of physical processes, involving generalizations of phase-number and energy-time uncertainty relations.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meetingJan 1, 20130 citations

Bipartite energy-time uncertainty relation and quantum error correction for metrology with noise

Philippe Faist, Mischa P. Woods, Victor V. Albert +3 more

Bulletin of the American Physical SocietyMar 16, 20210 citations

An ideal quantum clock and Principle of maximum force

Yu. L. Bolotin, V. A. Cherkaskiy, Anatoli Tur +1 more

We show that the space-time uncertainty relation for the quantum clock can be derived from the maximum force principle.

arXiv:1604.01945Apr 7, 20166 citations

Time-energy uncertainty relation for noisy quantum metrology

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Time-energy uncertainty relation for noisy quantum metrology

Abstract

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