Related papers: Quantum Parameter Estimation Uncertainty Relation
Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg…
The simultaneous quantum estimation of multiple parameters can provide a better precision than estimating them individually. This is an effect that is impossible classically. We review the rich background of multi-parameter quantum…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Difficult it is to formulate achievable sensitivity bounds for quantum multiparameter estimation. Consider a special case, one parameter from many: many parameters of a process are unknown; estimate a specific linear combination of these…
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…
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the…
Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
In practical applications like quantum sensing and quantum imaging, there is often a necessity to estimate multiple parameters simultaneously. Although the ultimate precision limits for single-parameter estimation are well established, the…
Single parameter estimation is known to benefit from extreme sensitivity to parameter changes in quantum critical systems. However, the simultaneous estimation of multiple parameters is generally limited due to the incompatibility arising…
We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can…
Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…