Related papers: Average of uncertainty-product for bounded observa…
In this paper, asymptotic behavior of the uncertainty product of Gauss-Weierstrass wavelet is investigated. It is shown that the uncertainty product is bounded from above, a feature that distinguishes Gauss-Weierstrass wavelet among other…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted…
We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
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…
In this paper we prove a nontrivial lower bound for the determinant of the covariance matrix of quantum mechanical observables, which was conjectured by Gibilisco, Isola and Imparato. The lower bound is given in terms of the commutator of…
Given a physical quantum system described by a Hilbert H, for any bounded quantum observable (a bounded self-adjoint operator) T it is possible to define several ''hidden observable'' functions f:H->R associated to T and for any quantum…
Any rule for identifying a quantum system's state within a set of two non-orthogonal pure states by a single measurement is flawed. It has a non-zero probability of either yielding the wrong result or leaving the query undecided. This also…
Inspired by the theory of quantum information, I use two non-Hermitian random matrix models - a weighted sum of circular unitary ensembles and a product of rectangular Ginibre unitary ensembles - as building blocks of three new products of…
We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size $N$ in $L$ orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate…
We construct an entanglement measure that coincides with the generalized concurrence for a general pure bipartite state based on wedge product. Moreover, we construct an entanglement measure for pure multi-qubit states, which are…
The canonical Robertson-Schr\"{o}dinger uncertainty relation provides a loose bound for the product of variances of two non-commuting observables. Recently, several tight forward and reverse uncertainty relations have been proved which go…
Rigorous assessment of the uncertainty is crucial to the utility of numerical simulation of Turbulent flow. The Turbulent flows are often stationary and ergodic, after some initial transient time. Therefore, the time averaged of a quantity…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
We present observable upper bounds of squared concurrence, which are the dual inequalities of the observable lower bounds introduced in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)] and [L. Aolita, A. Buchleitner and…
The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…