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Accurate time-delay measurement is at the core of many modern technologies. Here, we present a temporal-mode demultiplexing scheme that achieves the ultimate quantum precision for the simultaneous estimation of the temporal centroid, the time offset, and the relative intensities of an incoherent mixture of ultrashort pulses at the single-photon level. We experimentally resolve temporal separations ten times smaller than the pulse duration, as well as imbalanced intensities differing by a factor of $10^{2}$. This represents an improvement of more than an order of magnitude over the best standard methods based on intensity detection.
At the fundamental level, quantum communication is ultimately limited by noise. For instance, quantum signals cannot be amplified without the introduction of noise in the amplified states. Furthermore, photon loss reduces the signal-to-noise ratio, a
The ultimate precision limit in estimating the Larmor frequency of $N$ unentangled rotating spins is well established, and is highly important for magnetometers, gyroscopes and many other sensors. However this limit assumes perfect, single addressing
The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently
The orbital angular momentum L as an integer can be ultimately factorized as a product of prime numbers. We show here a close relation between the resolution of L and the classification of quantum states of an N-electron 2-dimensional system. In this
Bayesian methods which utilize Bayes theorem to update the knowledge of desired parameters after each measurement, are used in a wide range of quantum science. For various applications in quantum science, efficiently and accurately determining a quan