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Published August 2, 2017 | Supplemental Material + Submitted + Published
Journal Article Open

Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals


The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

Additional Information

© 2017 American Physical Society. Received 24 August 2016; published 2 August 2017. We would like to thank members of the LSC MQM, AIC, and QN groups for fruitful discussions. H. M. is supported by UK STFC Ernest Rutherford Fellowship (Grant No. ST/M005844/11). R. X. A. is supported by NSF Grant No. PHY-0757058. Y. M., B. P., and Y. C. are supported by NSF Grants No. PHY-1506453 and PHY-1612816. R. X. A., B. P., and Y. C. gratefully acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontier Center with support of the Gordon and Betty Moore Foundation.

Attached Files

Published - PhysRevLett.119.050801.pdf

Submitted - 1608.00766.pdf

Supplemental Material - supp.pdf


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