Related papers: Optimality of entropic uncertainty relations
A way to pose the entropic uncertainty principle for trace-preserving super-operators is presented. It is based on the notion of extremal unraveling of a super-operator. For given input state, different effects of each unraveling result in…
We formulate uncertainty relations for mutually unbiased bases and symmetric informationally complete measurements in terms of the R\'{e}nyi and Tsallis entropies. For arbitrary number of mutually unbiased bases in a finite-dimensional…
Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a…
The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of 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…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
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…
A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of…
Heisenberg's uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the…
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 Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
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…
Entropic uncertainty relations are quantitative characterizations of Heisenberg's uncertainty principle, which make use of an entropy measure to quantify uncertainty. In quantum cryptography, they are often used as convenient tools in…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
Uncertainty relations for more than two observables have found use in quantum information, though commonly known relations pertain to a pair of observables. We present novel uncertainty and certainty relations of state-independent form for…
We study how the entropic uncertainty relation for position and momentum conjugate variables is minimized in the subspace of one-dimensional antisymmetric wave functions. Based partially on numerical evidence and partially on analytical…
Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states…