Related papers: Quadrature Uncertainty and Information Entropy of …
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…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
The uncertainty principle bounds our ability to simultaneously predict two incompatible observables of a quantum particle. Assisted by a quantum memory to store the particle, this uncertainty could be reduced and quantified by a new…
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…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
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…
Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…
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…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
How violently do two quantum operators disagree? Different fields of physics feature different measures of incompatibility: (i) In quantum information theory, entropic uncertainty relations constrain measurement outcomes. (ii) In condensed…
Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
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…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…
We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with…
In this letter, the number-phase entropic uncertainty relation and the number-phase Wigner function of generalized coherent states associated to a few solvable quantum systems with nondegenerate spectra are studied. We also investigate time…
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…
The notion of weighted quantum entropy is reviewed and considered for bipartite and noncomposite quantum systems. The known for the weighted entropy information inequality (subadditivity condition) is extended to the case of indivisible…