Stochastic Waveform Estimation at the Fundamental Quantum Limit

Creators: Gardner, James W.^{1, 2}; Gefen, Tuvia²; Haine, Simon A.¹; Hope, Joseph J.¹; Preskill, John²; Chen, Yanbei²; McCuller, Lee²

1. Australian National University
2. California Institute of Technology

Abstract

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Acknowledgement

We thank the following people for their advice provided during this research: Rana Adhikari, Evan Hall, Thakur Giriraj Hiranandani, Konrad Lehnert, Katarzyna Macieszczak, Ian MacMillan, Patrick Meyers, Haixing Miao, Swadha Pandey, John Teufel, Mankei Tsang, Sander Vermeulen, Chris Whittle, and Sisi Zhou. We also thank the Caltech Chen Quantum Group and the ANU CGA Squeezer Group. In Fig. 1, we use component graphics from Ref. 121, with permission. The computations presented here were conducted in the Resnick High Performance Computing Center, a facility supported by Resnick Sustainability Institute at the California Institute of Technology. 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 U.S. National Science Foundation (NSF) Grant No. PHY-2011968. In addition, Y.C. acknowledges the support by the Simons Foundation (Award No. 568762) and the NSF Grant No. PHY-2309231. 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 Australian Research Council Future Fellowship Grant No. FT210100809. J.P. acknowledges support from the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research (Grants No. DE-NA0003525 and No. DE-SC0020290), the U.S. DOE, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the NSF (Grant No. PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. L.M.’s photon-counting effort on the GQuEST project is funded in part by the Heising-Simons Foundation through Grant No. 2022-3341. This paper has been assigned LIGO Document No. P2400069.

Data Availability

The data that supports our results uses Mathematica [122] and python [122-131] and is openly available online [132].

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