Related papers: Incorporating Heisenberg's Uncertainty Principle i…
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can~there be some trade-off relation between the…
The Heisenberg's error-disturbance relation is a cornerstone of quantum physics. It was recently shown to be not universally valid and two different approaches to reformulate it were proposed.The first one focuses on how error and…
The optimal quantum measurements for estimating individual parameters might be incompatible with each other so that they cannot be jointly performed. The tradeoff between the estimation precision for different parameters can be…
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…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
The observables of a noisy quantum system can be estimated by appropriately filtering the records of their continuous measurement. Such filtering is relevant for state estimation and measurement-based quantum feedback control. It is…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
We discuss the problem of finding the best measurement strategy for estimating the value of a quantum system parameter. In general the optimum quantum measurement, in the sense that it maximizes the quantum Fisher information and hence…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint…
We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is…
We identify precision limits for the simultaneous estimation of multiple parameters in multimode interferometers. Quantum strategies to enhance the multiparameter sensitivity are based on entanglement among particles, modes or combining…
Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's error-disturbance uncertainty relation can be violated…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for…