Related papers: Tight state-independent uncertainty relations for …
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…
The limitation on obtaining precise outcomes of measurements performed on two non-commuting observables of a particle as set by the uncertainty principle in its entropic form, can be reduced in the presence of quantum memory. We derive a…
Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\hat x$ and $\hat p$, quantum entropic…
A more general measurement disturbance uncertainty principle is presented in a Robertson-Schr\"odinger formulation. It is shown that it is stronger and having nicer properties than Ozawa's uncertainty relations. In particular is invariant…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted…
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…
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…
We obtain uncertainty and certainty relations of state-independent form for the three Pauli observables with use of the R\'enyi entropies of order $\alpha\in(0;1]$. It is shown that these entropic bounds are tight in the sense that they are…
We consider two (natural) families of observables $O_k$ for systems with dimension $d=3,4,5$: the spin observables $S_x$, $S_y$ and $S_z$, and the observables that have mutually unbiased bases as eigenstates. We derive tight entropic…
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions $d = 3$, $4$ and…
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…
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…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the…