Abstract
We study quantum frequency estimation forNqubits subjected to independent Markovian noise, via strategies based on time-continuous monitoring of the environment. Both physical intuition and an extended convexity property of the quantum Fisher information (QFI) suggest that these strategies are more effective than the standard ones based on the measurement of the unconditional state after the noisy evolution. Here we focus on initial GHZ states and on parallel or transverse noise. For parallel noise, i.e. dephasing, we show that perfectly efficient time-continuous photo-detection allows to recover the unitary (noiseless) QFI, and thus to obtain a Heisenberg scaling for every value of the monitoring time. For finite detection efficiency, one falls back to the noisy standard quantum limit scaling, but with a constant enhancement due to an effective reduced dephasing. Also in the transverse noise case we obtain that the Heisenberg scaling is recovered for perfectly efficient detectors, and we find that both homodyne and photo-detection based strategies are optimal. For finite detectors efficiency, our numerical simulations show that, as expected, an enhancement can be observed, but we cannot give any conclusive statement regarding the scaling. We finally describe in detail the stable and compact numerical algorithm that we have developed in order to evaluate the precision of such time-continuous estimation strategies, and that may find application in other quantum metrology schemes.
Highlights
Quantum metrology is one of the most promising fields within the realm of quantum technologies, with appli-The above result relies on the assumption of noiseless unitary dynamics, but the unavoidable interaction with the surrounding environment can have dramatic consequences on the performances of these protocols
We develop a stable and compact numerical algorithm that allows us to calculate the effective quantum Fisher information characterizing this kind of measurement strategy, and that will find application in quantum metrology problems beyond the ones considered in this paper
We can see that at lower efficiencies the curves tend to the unconditional quantum Fisher information (QFI) Q[ ⊥unc], while for perfect efficiency they coincide with QLω
Summary
Quantum metrology is one of the most promising fields within the realm of quantum technologies, with appli-The above result relies on the assumption of noiseless unitary dynamics, but the unavoidable interaction with the surrounding environment can have dramatic consequences on the performances of these protocols. Several attempts to circumvent these nogo theorems and obtain a superclassical scaling in the presence of noise have been pursued, exploiting timeinhomogeneous dynamics [10,11,12,13,14], noise with a particular geometry [15, 16], dynamical decoupling [17], and quantum error-correction protocols (or, more generally, the possibility to implement control Hamiltonians) [18,19,20,21,22,23,24,25,26]. Methods to calculate classical and quantum Cramer-Rao bounds for parameter estimation via time-continuous monitoring have been proposed [40,41,42,43,44], and put into action [45,46,47,48]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
