Limits of noisy quantum metrology with correlated qubits

by Mr Guiseppe Calabrese (ETHZ)

Friday 7 Mar 2025, 10:00 → 11:00 Europe/Zurich

WHGA/021

Quantum metrology aims to estimate unknown parameters with the highest possible precision. By leveraging quantum resources as probes, measurement accuracy can achieve the Heisenberg Limit (HL), where the estimation error scales as 1/n with the number of spatial or temporal resources, offering a quadratic improvement over the Standard Limit (SL) of 1/\sqrt{n}. However, noise fundamentally limits this advantage. For uncorrelated noise models, optimal performance typically requires costly resources such as real-time measurements and feed-forward QEC, noiseless ancillae or long-range entangled multi-probe states, making experimental implementations challenging.  

In this thesis, we investigate classically correlated noise models with restricted - specifically unitary - controls, and derive upper and lower bounds on the estimation precision, quantified by the Quantum Fisher Information (QFI). Our results show that correlations enhance metrological performance: perfect correlations allow the HL to be reached even without control operations, while in cases where only the SL is achievable, correlations still improve precision by increasing the QFI scaling constant. Finally, we present protocols that attain the optimal QFI scaling in different noise scenarios.