Related papers: Tight entropic uncertainty relations for systems w…
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…
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…
In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for R\'{e}nyi and Tsallis entropies besides the Shannon…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also…
We investigate the uncertainty principle for two successive projective measurements in terms of R\'enyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the…
One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $\ln d$. It has…
Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…
As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…
We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…
We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff…