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Coherent-state-based phase estimation is a fruitful testbed for the field of precision measurements since coherent states are robust to decoherence when compared with exotic quantum states. The seminal work done by Caves (https://doi.org/10.1103/PhysRevD.23.1693 , Phys. Rev. D 23, 1693 (1981)) stated that the phase sensitivity of a U(2) interferometer fed with a coherent state is limited by the shot-noise limit (SNL). In this Letter, we demonstrate that this bound is not conclusive sensitivity limit and can be broken when the measurement includes an external phase reference. The SNL can be surpassed by a factor of $sqrt{2}$ and the validity is supported through the calculation of quantum Fisher information. Additionally, we discuss other single-mode Gaussian inputs of which sensitivities are beyond the SNL. Our work shows potential applications for many metological scenarios, particularly when the measured samples immersed in great lossy environments or can withstand bright illumination.
Magneto-optical sensors including spin noise spectroscopies and magneto-optical Kerr effect microscopies are now ubiquitous tools for materials characterization that can provide new understanding of spin dynamics, hyperfine interactions, spin-orbit i
Photonic sensors have many applications in a range of physical settings, from measuring mechanical pressure in manufacturing to detecting protein concentration in biomedical samples. A variety of sensing approaches exist, and plasmonic systems in par
The displacement of micro-electro-mechanical-systems (MEMS) cantilevers is used to measure a broad variety of phenomena in devices ranging from force microscopes to biochemical sensors to thermal imaging systems. We demonstrate the first direct measu
Semiclassical methods can now explain many mesoscopic effects (shot-noise, conductance fluctuations, etc) in clean chaotic systems, such as chaotic quantum dots. In the deep classical limit (wavelength much less than system size) the Ehrenfest time (
A recent claim by Lieu et al that beam splitter intensity subtraction (or homodyne with one vacuum port) followed by high resolution sampling can lead to detection of brightness of thermal light at the shot noise limit is reexamined here. We confirm