Dimensional gain in sensing through higher-dimensional quantum spin chain

Abstract: Recent breakthroughs in quantum technology pave the way for extensive utilization of higher-dimensional quantum systems, which outperform their qubit counterparts in terms of capabilities and versatility. We present a framework for accurately predicting weak external magnetic fields using a higher-dimensional many-body quantum probe. We demonstrate that dimension serves as a valuable resource for quantum sensing when a transverse spin-s Ising chain interacts locally with a magnetic field whose strength has to be determined. We observe the distinct performance of sensors for spin chains with half-integer and integer spins. Furthermore, we highlight that the time duration appropriate for quantum-enhanced sensing increases with the increase of dimension. Additionally, we observe that, in addition to nearest-neighbor interactions, incorporating interactions between the next nearest-neighbor sites increases sensing precision, particularly for spin chains with integer spins. We also prove the dimensional-dependence of the bound on quantum Fisher information which provides the limit on the precision in estimating parameters.