Achieving the Fundamental Quantum Limit of Linear Waveform Estimation

Creators: Gardner, James W.; Gefen, Tuvia; Haine, Simon A.; Hope, Joseph J.; Chen, Yanbei¹

1. California Institute of Technology

Abstract

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation quantum Cramér-Rao bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cramér-Rao bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for postmerger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal’s power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of $\sqrt{2}$ using this nonstationary measurement.

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Acknowledgement

We thank the following individuals and groups for their advice provided during this research: L. McCuller, S. Kotler, J. Preskill, Z. Mehdi, A. Markowitz, D. Ganapathy, S. Zhou, L. Sun, R. X. Adhikari, the Caltech Y. Chen Quantum Group, and the ANU CGA Squeezer Group. We use component graphics from Ref. [70] with permission. This research is supported by the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (Project No. CE170100004). J. W. G. and this research are supported by an Australian Government Research Training Program (RTP) Scholarship and also partially supported by the US NSF Grant No. PHY-2011968. In addition, Y. C. acknowledges the support by the Simons Foundation (Grant No. 568762). T. G. acknowledges funding provided by the Institute for Quantum Information and Matter and the Quantum Science and Technology Scholarship of the Israel Council for Higher Education. S. A. H. acknowledges support through an Australian Research Council Future Fellowship Grant No. FT210100809. This Letter has been assigned LIGO Document No. P2300096.

Code Availability

Our code is available online [63] and was written using Mathematica [64] and python [65–69].

Data Availability

Supplemental Material

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