On uncertainty relations and entanglement detection with mutually unbiased measurements

Abstract

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

13 pages, no figures. Minor improvements. Typos fixed

References in corpus (6)

• Heisenberg's Uncertainty Principle
• Entropic uncertainty relation for mutually unbiased bases
• Entanglement detection using mutually unbiased measurements
• Entanglement, Purity, and Information Entropies in Continuous Variable Systems
• A transform of complementary aspects with applications to entropic uncertainty relations
• Inequalities detecting entanglement for arbitrary bipartite systems