Related papers: Variance uncertainty relations without covariances…
Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
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…
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range…
Bell nonlocality and uncertainty relations are distinct features of quantum theory from classical physics. Bell nonlocality concerns the correlation strength among local observables on different quantum particles, whereas the uncertainty…
The uncertainty relations (URs) of two arbitrary Hermitian and non-Hermitian incompatible operators represented by the product of variances have been confirmed theoretically and experimentally in various physical systems. However, the lower…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
The generalized uncertainty connection between the fluctuations of a quantum observable and its temporal derivative is derived in this study, we demonstrate that the product of an observable's uncertainties and its time derivative is…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…
A smooth function of the second moments of $N$ continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously…
Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…
Recently, Maccone and Pati [Phys. Rev. Lett. {\bf 113}, 260401 (2014)] derived few inequalities among variances of incompatible operators which they called stronger uncertainty relations, stronger than Heisenberg-Robertson or Schrodinger…