Bias in error-corrected quantum sensing*

Quantum-enhanced sensors use quantum systems and effects to sense an external signal in their environment, such as electromagnetic fields, temperature or pressure. They also, however, experience decoherence due to this same environment, which limits their sensitivity in practice. Quantum error correction (QEC) can enhance this sensitivity by suppressing decoherence [1].

We demonstrate that, in addition, error correction of a quantum sensor introduces a side-effect: in realistic settings, the finite strength of QEC biases the sensor's output [2]. If unaccounted for, this bias can systematically reduce the sensor’s performance in experiment, and give misleading values for the minimum detectable signal in theory. We analyze this effect in the setting of continuous-time QEC, showing both how one can remedy the bias through post-processing of measurement data, and how incorrect results can arise when one does not.

[1] F. Reiter, A. S. Sørensen, P. Zoller, and C. A. Muschik. Dissipative quantum error correction and application to quantum sensing with trapped ions, Nat. Commun. 8, 1822 (2017).

[2] I. Rojkov, D. Layden, P. Cappellaro, J. Home, and F. Reiter, Bias in error-corrected quantum sensing, arXiv: 2101.05817 (2021).