Quantum metrology with finite-energy GKP states*

Finite-energy GKP states have been shown to be sensitive single-mode displacements sensors [1]. Moreover, quantum error correction has been proposed as a tool to enhanced the accuracy of metrology protocols [2]. Here, we explore the connection between these concepts and study the use of stabilized quantum error corrected finite-energy GKP states as quantum sensors. We analyze their use as single-mode displacement sensors, and provide protocols to improve the measurement sensitivity achievable with uncorrected finite-energy GKP states. Going beyond the single-mode scenario, we explore multi-mode GKP sensitivity improvements over their single-mode counterparts. Finally, we explore potential applications.

[1] Duivenvoorden, K., Terhal, B. M., & Weigand, D. Phys. Rev. A 95, 012305 (2017).

[2] Kessler, E. M., Lovchinsky, I., Sushkov, A. O., & Lukin, M. D. Phys. Rev. Lett. 112, 150802 (2014).