Related papers: Kramers-Kronig relations and precision limits in q…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this…
We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…
Quantum mechanics establishes the ultimate limit to the scaling of the precision on any parameter, by iden- tifying optimal probe states and measurements. While this paradigm is, at least in principle, adequate for the metrology of quantum…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
In quantum phase estimation, the Heisenberg limit provides the ultimate accuracy over quasi-classical estimation procedures. However, realizing this limit hinges upon both the detection strategy employed for output measurements and the…
Phase measurement constitutes a key task in many fields of science, both in the classical and quantum regime. The higher precision of such measurement offers significant advances, and can also be utilised to achieve finer estimates for…
We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…
Quantum control plays a crucial role in enhancing precision scaling for quantum sensing. However, most existing protocols require perfect control, even though real-world devices inevitably have control imperfections. Here, we consider a…
The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
For the last 20 years, the question of what are the fundamental capabilities of quantum precision measurements has sparked a lively debate throughout the scientific community. Typically, the ultimate limits in quantum metrology are…
Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…
We address the estimation of the loss parameter of a bosonic channel probed by Gaussian signals. We derive the ultimate quantum bound on precision and show that no improvement may be obtained by having access to the environment degrees of…
This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical…
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…
We find the optimal scheme for quantum phase estimation in the presence of loss when no a priori knowledge on the estimated phase is available. We prove analytically an explicit lower bound on estimation uncertainty, which shows that, as a…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…