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<jats:p>We have measured the geopotential difference between two locations separated by 457 km by comparison of two optical lattice clocks via an interferometric fiber link, utilizing the gravitational redshift of the clock transition frequency. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:msup><a:mi/><a:mn>87</a:mn></a:msup><a:mi>Sr</a:mi></a:math> clocks have been compared side-by-side before and after one of the clocks was moved to the remote location. The chronometrically measured geopotential difference of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mn>3918.1</d:mn><d:mo stretchy="false">(</d:mo><d:mn>2.6</d:mn><d:mo stretchy="false">)</d:mo><d:mspace width="0.2em"/><d:msup><d:mrow><d:mi mathvariant="normal">m</d:mi></d:mrow><d:mn>2</d:mn></d:msup><d:mspace width="0.2em"/><d:msup><d:mrow><d:mi mathvariant="normal">s</d:mi></d:mrow><d:mrow><d:mrow><d:mo>−</d:mo><d:mn>2</d:mn></d:mrow></d:mrow></d:msup></d:math> agrees with an independent geodetic determination of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><m:mn>3915.88</m:mn><m:mo stretchy="false">(</m:mo><m:mn>0.30</m:mn><m:mo stretchy="false">)</m:mo><m:mspace width="0.2em"/><m:msup><m:mrow><m:mi mathvariant="normal">m</m:mi></m:mrow><m:mn>2</m:mn></m:msup><m:mspace width="0.2em"/><m:msup><m:mrow><m:mi mathvariant="normal">s</m:mi></m:mrow><m:mrow><m:mo>−</m:mo><m:mn>2</m:mn></m:mrow></m:msup></m:math>. The uncertainty of the chronometric geopotential difference is equivalent to an uncertainty of <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><v:mn>27</v:mn><v:mspace width="0.2em"/><v:mi>cm</v:mi></v:math> in height.</jats:p> <jats:sec> <jats:title/> <jats:supplementary-material> <jats:permissions> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material> </jats:sec>

<jats:p>The task of sensing the presence of a target object using a weak light source is challenging when the object is embedded in a noisy environment. One possibility is to use quantum illumination to do this, as it can outperform classical illumination in determining the object presence and range. This advantage persists even when both classical and quantum illumination are restricted to identical suboptimal object-detection measurements based on nonsimultaneous, phase-insensitive coincidence counts. Motivated by realistic experimental protocols, we present a theoretical framework for analyzing coincident multishot data with simple detectors. This approach allows for the often-overlooked noncoincidence data to be included, as well as providing a calibration-free threshold for inferring an object’s presence and range, enabling a fair comparison between different detection regimes. Our results quantify the advantage of quantum over classical illumination when performing target discrimination in a noisy thermal environment, including estimating the number of shots required to detect a target with a given confidence level.</jats:p> <jats:sec> <jats:title/> <jats:supplementary-material> <jats:permissions> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material> </jats:sec>