Uncertainty Relations in the Presence of Quantum Memory for Mutually Unbiased Measurements

Abstract

In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased measurements. Our primary result is an equality between the amount of uncertainty for a set of measurements and the amount of entanglement of the measured state, both of which are quantified by the conditional collision entropy. Implications of this equality relation are discussed. We further show that similar equality relation can be obtained for generalized symmetric informationally complete measurements. We also derive an interesting equality for arbitrary orthogonal basis of the space of Hermitian, traceless operators.

arXiv comment8 pages, comments are welcome!

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Cited by in corpus (4)

• Entropic uncertainty relations for SIC-POVMs and MUMs
• Symmetric measurement-induced lower bounds of concurrence
• Generalization of Pauli channels through mutually unbiased measurements
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases