Optimal upper bound of entropic uncertainty relation for mutually unbiased bases

Abstract

We have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of $N$ MUBs. Our result is valid for any state when $N$ is $d+1$, where $d$ is the dimension of the related system. We provide a quantitative criterion for the extendibilty of MUBs. In addition, we have applied our result to the mutual information of $d+1$ observables conditioned with a classical memory.

10 pages, no figures, regular article

References in corpus (3)

• Entropic uncertainty relation for mutually unbiased bases
• Improved tripartite uncertainty relation with quantum memory
• Uncertainty relation in Schwarzschild spacetime

Cited by in corpus (2)

• On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables