Środowiskowe Seminarium z Informacji i Technologii Kwantowych
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2022-06-09 (11:15) 
Giovanni Di Fresco (Università di Palermo)
Can compatibility in multi-parameter estimation schemes be induced by criticality?
The Seminar will be ONLINE ONLY using ZOOM under the following link: https://zoom.us/j/92894130767 (Passcode: R6Vx6E).
It is known that many-body systems near a quantum phase transition (QPT) exhibit severalproperties which makes them appealing for metrological purposes. Indeed, it is now wellestablished and widely used that the divergences of the quantum Fisher informationobserved near a QPT can be used to increase the precision in the estimation of a parameter.Meanwhile, when it comes to the simultaneous estimation of multiple parameters, thebenefits of criticality are much harder to analyze due to possible incompatibilities arising fromthe Heisenberg uncertainty. This involves the use of quite convoluted quantities, as theHolevo-Cramer-Rao bound, which are far from straightforward to evaluate in systems ofinterest. Here we study the quantumness (R), a scalar index, which provides an asymptoticbound on the compatibility of a metrological scheme. The advantage of this approach is thatR can be easily evaluated once the Quantum Fisher information and the mean Uhmlanncurvature are known. Moreover, a scaling analysis of R reveals that many-body criticalitiesgenerally improve the compatibility in a multi-parameter framework. In fact, we show thatthe quantum critical point is a good place to look for compatibility. We corroborate thesegeneral statements with numerical simulations performed on some representative systems,such as Ising chain and XY chain, in which we find this positive criticality effects
It is known that many-body systems near a quantum phase transition (QPT) exhibit severalproperties which makes them appealing for metrological purposes. Indeed, it is now wellestablished and widely used that the divergences of the quantum Fisher informationobserved near a QPT can be used to increase the precision in the estimation of a parameter.Meanwhile, when it comes to the simultaneous estimation of multiple parameters, thebenefits of criticality are much harder to analyze due to possible incompatibilities arising fromthe Heisenberg uncertainty. This involves the use of quite convoluted quantities, as theHolevo-Cramer-Rao bound, which are far from straightforward to evaluate in systems ofinterest. Here we study the quantumness (R), a scalar index, which provides an asymptoticbound on the compatibility of a metrological scheme. The advantage of this approach is thatR can be easily evaluated once the Quantum Fisher information and the mean Uhmlanncurvature are known. Moreover, a scaling analysis of R reveals that many-body criticalitiesgenerally improve the compatibility in a multi-parameter framework. In fact, we show thatthe quantum critical point is a good place to look for compatibility. We corroborate thesegeneral statements with numerical simulations performed on some representative systems,such as Ising chain and XY chain, in which we find this positive criticality effects