Entropic Uncertainty Relations in Quantum Physics

Entropic uncertainty relations—a survey

Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, little is known about entropic uncertainty relations with more than two measurement settings. In the present survey, we review known resu...

A transform of complementary aspects with applications to entropic uncertainty relations

Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols, they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases MUBs in dimension d=2n, which have particularly beautiful symmetry properties derived from the Clifford algebra. More precisely, we show that there exists a unitary tran...

Entropic Uncertainty Relations in Quantum Physics

Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra

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 evolution of ”number-phase entropic uncertainty” and ”Wigner function” of the considered physical systems with the help of temporally stable Gazeau-Klau...

Entropic uncertainty relations for multiple measurements

We present the entropic uncertainty relations for multiple measurement settings which demonstrate the uncertainty principle of quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory, and can be proven by a unified method. Our results recover some well known entropic uncertainty relations for two observables, which show the unce...