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One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes that attain that precision. In this article we present a…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
In the scenario of the probe-ancilla interaction, we propose a quantum metrology protocol by the unconditional measurement on the ancillary qubit after an optimized period of joint evolution from product state. Its key element is the…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg Limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can…
We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications…
We provide general bounds of phase estimation sensitivity in linear two-mode interferometers. We consider probe states with a fluctuating total number of particles. With incoherent mixtures of state with different total number of particles,…
We review, correct, and develop an algorithm which determines arbitrary Quantum Bounds, based on the seminal work of Tsirelson [Lett. Math. Phys. 4, 93 (1980)]. The potential of this algorithm is demonstrated by deriving both new…
Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the…
We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on…
Quantum entanglement has the potential to revolutionize the entire field of interferometric sensing by providing many orders of magnitude improvement in interferometer sensitivity. The quantum-entangled particle interferometer approach is…
Classical measurement strategies in many areas are approaching their maximum resolution and sensitivity levels, but these levels often still fall far short of the ultimate limits allowed by the laws of physics. To go further, strategies…
Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as…
Heisenberg scaling characterizes the ultimate precision of parameter estimation enabled by quantum mechanics, which represents an important quantum advantage of both theoretical and technological interest. Here, we study the attainability…