Multiqubit matter-wave interferometry under decoherence and the Heisenberg scaling recovery

TL;DR

This paper evaluates multiqubit matter-wave interferometry under realistic noise conditions, revealing that decoherence can diminish quantum advantages and exploring quantum error correction as a potential solution.

Contribution

It provides the first comprehensive assessment of multiqubit matter-wave interferometry under decoherence, highlighting the limitations of entangled states and proposing error correction to recover Heisenberg scaling.

Findings

Optimal precision decreases with particle number under dephasing.

GHZ states lose quantum Fisher information in large-N regimes.

Quantum error correction can potentially restore Heisenberg scaling.

Abstract

Most matter-wave interferometry (MWI) schemes for quantum sensing are so far evaluated in ideal situations without noises. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noises. We find that for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes \emph{decreases} with increasing the particle number $N$, for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-type interferometers. We initiate the analyses by investigating the optimal precision of multiqubit Sagnac atom interferometry for rotation sensing. And we show that due to the competition between the unconventional interrogation-time quadratic phase accumulation and the exponential dephasing processes, the Greenberger-Horne-Zeilinger (GHZ) state, which is the optimal input state in noiseless scenarios, leads to vanishing quantum Fisher information in the large-$N$ regime. Then our assessments are further extended to generic MWI schemes for quantum sensing with entangled states and under decoherence. Finally, a quantum error-correction logical GHZ state is tentatively analyzed, which could have the potential to recover the Heisenberg scaling and improve the sensitivity.