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The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…
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…
We revisit, in the framework of Mach-Zehnder interferometry, the connection between the complementarity and uncertainty principles of quantum mechanics. Specifically, we show that, for a pair of suitably chosen observables, the trade-off…
The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
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…
Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…
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…
We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…